{"as_of":"2026-08-10T14:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2b9e775151572a4a8b0f524d1879452d2cc1ffa8d64d01c6764af93870a3e543","coverage":[{"denominator":86,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":86,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-02T19:26:59.341194Z","state":"measured"},{"denominator":86,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":86,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.00257/citation-record","integrity":"/paper/2607.00257/integrity","json":"/paper/2607.00257/citation-record.json","paper":"/paper/2607.00257"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.409537Z","title":"Exploration and prediction of fluid dynamical systems using auto-encoder technology.Physics of Fluids, 32(6), 2020","venue":null,"work_id":"e2feb443-fda8-45ef-9838-eeac114058f8","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:20a36c371d88ae692a4dd63f25ea8bcd598f812459b1baf13ed98eec130be088","observation_id":"e47d2eb6-4606-4e76-a585-f9ba9815e877","resolution":{"observed_at":"2026-07-05T21:11:29.411039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.407554Z","title":"Kernel ridge regression hybrid method for wheat yield prediction with satellite-derived predictors.Remote Sensing, 14(5):1136, 2022","venue":null,"work_id":"159ce967-cb56-4c74-9b59-1a04c5cca5fd","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:b783ad0008067f3d988975e9e35e176a33a1d3a31f82e186afe9e79504ce7d7a","observation_id":"4d77f71c-6407-4913-a669-92a6c20292e0","resolution":{"observed_at":"2026-07-05T21:11:29.409012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.450161Z","title":"Sampling procedures in function spaces and asymptotic equivalence with Shannon’ s sampling theory.Numerical functional analysis and optimization, 15(1-2):1–21, 1994","venue":null,"work_id":"93492a98-7f98-488c-ab82-b2c3307fcb1d","year":1994},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:b70eb3d3f2a06bd92c02e940e340590ae3d7018d1a55584c927ca14133de79e4","observation_id":"6b104e3b-ef2c-4259-9fa3-47db07f82241","resolution":{"observed_at":"2026-07-05T21:11:29.451467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.454117Z","title":"Complete ensemble empirical mode decomposition hybridized with random forest and kernel ridge regression model for monthly rainfall forecasts","venue":null,"work_id":"26b854a6-00ce-48d4-82e1-c9789bbb0276","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9645f4e6e72a18bc0884b006397c5ffb3f1e96261a1054419034269c63c844ef","observation_id":"3abc6691-6a23-4a77-91d8-5e524cc9c236","resolution":{"observed_at":"2026-07-05T21:11:29.455470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.463422Z","title":"Dynamic data-driven local traffic state estimation and prediction.Transportation Research Part C: Emerging Technologies, 34:89–107, 2013","venue":null,"work_id":"c9d425e9-912f-486f-9bab-e9805163a206","year":2013},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:3f0ad190c7ff9f6a703b75fe0d8f3dca04833529b3c8643d4050282d24ebffab","observation_id":"40478cc2-540f-431d-9474-833f3b064d7c","resolution":{"observed_at":"2026-07-05T21:11:29.464728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.446372Z","title":"Data-driven analysis and forecasting of highway traffic dynamics.Nature communications, 11(1):2090, 2020","venue":null,"work_id":"7691e2c3-9acd-4767-8f6a-748111e5a533","year":2090},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:0c0a09f767dd9abdd9e1dfbe2e9d36eb0ff54bb5458fde9e509ca65c75ca1b4c","observation_id":"8602b7e7-4a44-4bde-b921-5fd762dea16f","resolution":{"observed_at":"2026-07-05T21:11:29.447641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.374870Z","title":"Approximation error for quasi-interpolators and (multi-) wavelet expansions","venue":null,"work_id":"2f5d14bd-4f5a-409a-a1fb-196ac6862cdf","year":1999},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9e94ed745fceb00b0d801f648712f1e7cc5945bbeec078a41a84c9826f865dd5","observation_id":"0dab44d1-3495-4a7d-ad7e-305f27f0b81a","resolution":{"observed_at":"2026-07-05T21:11:29.376154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.421389Z","title":"Weak form-based data-driven modeling: computationally efficient and noise robust equation learning and parameter inference","venue":null,"work_id":"e2782f4f-55a9-4167-8019-f3e3c8788fb7","year":2024},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:19608e15ea60fb9062c11f026bb2db804ad866ae8b58e113716fd9e747d0daf0","observation_id":"a176d9c3-dfa5-4509-970f-95dde671644a","resolution":{"observed_at":"2026-07-05T21:11:29.423202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.336059Z","title":"John Wiley & Sons","venue":null,"work_id":"71e9346f-4650-40db-854e-68c2255d91ec","year":2015},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:d4cdca7aba86aea203a371c0cc8e67493f814dc9571fbe2ec7bf3c027e2c9123","observation_id":"3e77c90b-df7c-491e-8e02-0bf43c566fb5","resolution":{"observed_at":"2026-07-05T21:11:29.337195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.456180Z","title":"Predicting regime changes and durations in Lorenz’ s atmospheric convection model.Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(10), 2020","venue":null,"work_id":"126aa55b-28e3-452f-a3bb-5d98e201faac","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:5e36b9d7b69877f8c9063d2af7d3fa4feac33dddb028762bd8ef4d134e5d0bef","observation_id":"8965524d-2ffd-45b0-848e-0481f83f71aa","resolution":{"observed_at":"2026-07-05T21:11:29.457469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.326356Z","title":"Cambridge University Press","venue":null,"work_id":"6e5ebb5a-a737-4058-8977-6adfb630334e","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:de336a0603d17f96dc9e3e45470f7d7509fab93d75af2e45d680262eeee87998","observation_id":"39e6c99d-7f80-44aa-a32b-fc18770aaf1c","resolution":{"observed_at":"2026-07-05T21:11:29.327399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.327988Z","title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the national academy of sciences, 113(15):3932– 3937","venue":null,"work_id":"9c7a0580-d192-4f6d-9380-f8337c05f8fb","year":2016},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:4354612e1d9ad9e0e311fff02b2abfb2d2c12b57198f5e676001725e6378f4da","observation_id":"08ef3dac-1b02-43f0-9384-d96368f538a7","resolution":{"observed_at":"2026-07-05T21:11:29.329264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.393176Z","title":"Sparse identification of nonlinear dynamics with control (SINDYc).IFAC-PapersOnLine, 49(18):710–715, 2016","venue":null,"work_id":"dad53709-4418-409a-b5c4-3596447fea6c","year":2016},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:76b3e8ed2632143ac40eff24f09a89dbfcf22d2d772b6fd76d2bce0be714b22a","observation_id":"f23d3284-e518-4ab7-ad22-4bdbba885cb1","resolution":{"observed_at":"2026-07-05T21:11:29.394548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.324299Z","title":"An intelligent system for financial time series prediction combining dynami- cal systems theory, fractal theory, and statistical methods","venue":null,"work_id":"53a9ed1d-2c2a-4974-82cb-cd253f5ddaa8","year":1995},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:c5c0a3922438eda98fd6eb84f7a206b91ac71c4b1a49ea8564ef8133f9c83388","observation_id":"19ea7cd7-617c-419d-b2a4-b92e72bf7644","resolution":{"observed_at":"2026-07-05T21:11:29.325782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T04:35:57.925491Z","title":"Neural ordinary differential equations.Advances in neural information processing systems, 31","venue":null,"work_id":"32de569a-cbec-44d8-a3c1-0ec3a37b8cc3","year":2018},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:e0cec4d5d9f9a8b90a12fff54e40431ef0e361d38bdd18ebe4625b7a70328172","observation_id":"6c9e0fe8-51e4-470d-a112-9a127f64ce95","resolution":{"observed_at":"2026-07-05T21:11:29.401562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.395042Z","title":"Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review.IEEE/CAA Journal of Automatica Sinica, 10(6):1361–1387, 2023","venue":null,"work_id":"51c187a6-25c0-48f2-8bb7-ac1647264b83","year":2023},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:cdbe191a095ed8f14c542fc75cdd551bcde31510cc2c98555b2acc06482534ab","observation_id":"78a02c3b-0372-4335-a111-51106c9c94ef","resolution":{"observed_at":"2026-07-05T21:11:29.397178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.389395Z","title":"From reliable weather forecasts to skilful climate response: A dynamical systems approach.Quarterly Journal of the Royal Meteorological Society, 145(720):1052–1069, 2019","venue":null,"work_id":"a59c0200-50bf-4ed6-baeb-36508f4b459f","year":2019},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:689bde09a0ebda1f16d5f4be0f66a635e6824e0ac019d799f99ed24483b90c67","observation_id":"f9f16d87-ebcf-4b00-b30d-3765c7bad753","resolution":{"observed_at":"2026-07-05T21:11:29.390726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T19:05:31.286246Z","title":"Diffusion maps.Applied and computational harmonic analysis, 21(1):5–30","venue":null,"work_id":"bf6a4752-ffdc-443f-87a4-56f244e1b19d","year":2006},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:cccdb8c1b2d548d9ace4568c8dc7bc8c756290172843b52861a46d9480e466f7","observation_id":"ef50d322-e1b6-489f-815b-a34bf9a5d2de","resolution":{"observed_at":"2026-07-05T21:11:29.339132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.345422Z","title":"Graph Laplacian tomography from unknown random projections.IEEE Transactions on Image Processing, 17(10):1891–1899, 2008","venue":null,"work_id":"2922fa9c-25ed-4d28-935d-100dbcfebba5","year":2008},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:0b86ea61a31b547abacb2fca253ddd259d884dfd4618eaa9b837587c4a760722","observation_id":"593a0f53-8889-4353-81fc-53cee9e7c777","resolution":{"observed_at":"2026-07-05T21:11:29.346748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.332239Z","title":"The mpedmd algorithm for data-driven computations of measure-preserving dynamical systems.SIAM Journal on Numerical Analysis, 61(3):1585–1608, 2023","venue":null,"work_id":"15771310-9003-4256-9d56-34607ff089be","year":2023},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:58a8c97a5c013351a2498d135f141a568421d9f9154d1664be48afd0c72cfe35","observation_id":"b6fd4ff3-ff34-4811-a703-ca81f9d98ad3","resolution":{"observed_at":"2026-07-05T21:11:29.333654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.376717Z","title":"Residual dynamic mode decomposition: robust and verified Koopmanism.Journal of Fluid Mechanics, 955:A21, 2023","venue":null,"work_id":"536b329f-87ff-4f4b-941d-409569947ae8","year":2023},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:b6793d96db10157e66b84a6159513361e9ed9080768b8f8e0e9ab25664002936","observation_id":"5b372176-cd5e-4f06-866d-545799d5bf21","resolution":{"observed_at":"2026-07-05T21:11:29.378149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.334213Z","title":"Lyapunov exponents of the Kuramoto–Sivashinsky PDE.The ANZIAM Journal, 61(3):270–285, 2019","venue":null,"work_id":"e853e166-9925-4875-8613-230105deb9ea","year":2019},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:a30673b835fefa0e9f591ef4ee388f508fe141f80a6d9301f8039c079506cfcb","observation_id":"d9ac407c-05ee-4e08-b908-0719e65aaa53","resolution":{"observed_at":"2026-07-05T21:11:29.335464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.380857Z","title":"Combining physics-based and data-driven modeling in well construction: Hybrid fluid dynamics modeling.Journal of Natural Gas Science and Engineering, 97:104348, 2022","venue":null,"work_id":"b30f5e07-0a79-4708-b3ef-051d5ed9db63","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:365f19d02db2ffdf590cc9eb22ebb28391d004740c9eadb3e5fb4408eddb16a4","observation_id":"bea5b47d-c781-4962-b8c7-7eee397c1e4e","resolution":{"observed_at":"2026-07-05T21:11:29.382240Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.370768Z","title":"Nonlinear forecasting with many predictors using kernel ridge regression.International Journal of Forecasting, 32(3):736–753, 2016","venue":null,"work_id":"66be4d57-9075-47d7-ad46-fc40fa0fafd4","year":2016},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:d8beb9cdddb6f4fb924a0f1ff29c92317ee3cb575ea465c5dbe493da738095d7","observation_id":"76bd2fc1-d63d-4cdf-a489-cd3d1ff193f9","resolution":{"observed_at":"2026-07-05T21:11:29.372228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.368179Z","title":"Data-driven discovery of intrinsic dynamics.Nature Machine Intelli- gence, 4(12):1113–1120, 2022","venue":null,"work_id":"f7e9d65e-4c08-4060-beb9-0c1ff3ad105e","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:f5fd1fdf7d76f08e14fb9acf3de4067eb69bd7355b9516e6ad4dce62d3fe70a7","observation_id":"d0867e3e-5441-4bfb-b1bb-ac5209137a66","resolution":{"observed_at":"2026-07-05T21:11:29.369840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.366142Z","title":"Next generation reservoir computing","venue":null,"work_id":"a69880f7-af10-4958-9de6-fb4258b2cb76","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:76390346cabae3296be7ce58066565bc958c0c49258b500ec160db69562038a7","observation_id":"3a8573fa-3501-4f3a-b70f-f40bf1bafdd3","resolution":{"observed_at":"2026-07-05T21:11:29.367526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.372932Z","title":"Data-driven prediction in dynamical systems: recent developments","venue":null,"work_id":"a0fa5684-f013-475f-bc38-de3f31aa4edc","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:1054d1963011c98009bfff7fb465cf069add8cb62981b2b8ff9c9779a52cbfad","observation_id":"7edaf317-f59e-4531-80d2-1de958005a65","resolution":{"observed_at":"2026-07-05T21:11:29.374188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.384985Z","title":"Learning dynamics from large biological data sets: machine learning meets systems biology.Current Opinion in Systems Biology, 22:1–7, 2020","venue":null,"work_id":"aa7e5378-e2a9-41cf-9f16-3791dd456d67","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:0cc99e2ae63a2643653c086deb4201e4a6b2c35c475745ba827dced83c7ce373","observation_id":"c99bb05d-b8bc-4330-bea6-f3f74e0547b0","resolution":{"observed_at":"2026-07-05T21:11:29.386714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.322361Z","title":"PhD thesis, University of the Balearic Islands (UIB); Institute for Cross-Disciplinary Physics and Complex Systems, 2024","venue":null,"work_id":"781b364f-8744-410e-86d9-40d36255b3da","year":2024},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9f80823868ef3a05d34880ef7bca97e32009d68c212f637ecd043a50e7198564","observation_id":"cc617ec7-b90b-453f-8871-04f988ab2c74","resolution":{"observed_at":"2026-07-05T21:11:29.323658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T13:47:06.750860Z","title":"Gaussian process priors with uncertain inputs application to multiple-step ahead time series forecasting.Advances in neural information processing systems, 15, 2002","venue":null,"work_id":"6e71f721-abfb-4aab-858d-1c078136617d","year":2002},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:e173033e2e23123c454f4e4f426f9f8d3f7b1f22cdcdae9f47da8a319fa5fa0a","observation_id":"47e765ec-3c51-44c6-a3e9-47d1fb346e8d","resolution":{"observed_at":"2026-07-05T21:11:29.399623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.404977Z","title":null,"venue":null,"work_id":"8a52145e-9221-45b9-8131-d99091279202","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:6169f36d134dbe4a23d9aff08c99b1fcb12079b05a2b2f887cc88353af2b729f","observation_id":"4895b99a-500a-4d89-8153-123e7e848f0b","resolution":{"observed_at":"2026-07-05T21:11:29.406281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.465267Z","title":"Supervised learning from noisy observations: Combining machine- learning techniques with data assimilation.Physica D: Nonlinear Phenomena, 423:132911, 2021","venue":null,"work_id":"61c07b4a-8091-4a07-b6c9-374b85ca7cbb","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:eeae1d6032abd59cc69a37e14d363bc0c19e99c14e3d1d8fa1cc0fa1a2e0e26e","observation_id":"ba67fa10-c00d-4cd5-b0e1-b6d2a5cf46b5","resolution":{"observed_at":"2026-07-05T21:11:29.467046Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2205.09479","last_updated":"2022-05-19T11:24:41Z","snapshot_observed_at":"2026-07-06T13:11:32.691554Z","submitted_at":"2022-05-19T11:24:41Z","title":"Neural ODEs with Irregular and Noisy Data","version":1},"cited_work":{"arxiv_id":"2205.09479","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2205.09479","snapshot_observed_at":"2026-07-02T19:27:18.452298Z","title":"Neural ODEs with irregular and noisy data.arXiv preprint arXiv:2205.09479, 2022","venue":null,"work_id":"f7123121-f949-41dd-9607-9a7b02c56feb","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"cited_paper":"/paper/2205.09479","citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:2863c400683806fa3fe8251b1ab3cd99f46220a14be0aae253e2df37a5263fc6","observation_id":"e633fe41-2eb0-4cdd-90e8-a946d9a6ee87","resolution":{"observed_at":"2026-07-02T19:27:18.453749Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.467622Z","title":"Diffusion maps kernel ridge regression.arXiv preprint, in preparation, 2026","venue":null,"work_id":"5006b197-af6c-4255-86e6-33a045f1ca57","year":2026},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:47b76d240f4c7fb809beff97b60c5dcf9e4c9a611a1ea71afee9e8997cf43887","observation_id":"f90437c9-6167-4712-a7d7-3df8fc612817","resolution":{"observed_at":"2026-07-05T21:11:29.468930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T02:34:28.052628Z","title":"Long short-term memory.Neural computation, 9(8):1735–1780","venue":null,"work_id":"ef918d76-ef1d-4ba0-805f-48bb2ff82b3a","year":1997},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:89fafd36f52ca63f54228ef9271d09cb4f4c08ee7c65a300f96b5fabadcae626","observation_id":"866e789f-ce6e-453e-a559-c888f3093be1","resolution":{"observed_at":"2026-07-05T21:11:29.356772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.359481Z","title":"Learning vector fields of differential equations on manifolds with geometrically constrained operator-valued kernels","venue":null,"work_id":"cb1dc97c-2dd9-423f-a5a9-60a0a6ffe741","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:8440813c936e99d74d5ac39d927e9d7ed7c33df6a1c6d0333c7c40043837e4fd","observation_id":"7cac1aec-0601-4401-a33d-1e952bb5ef6e","resolution":{"observed_at":"2026-07-05T21:11:29.361222Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.343578Z","title":"A dynamic neural network architecture with immunology inspired optimization for weather data forecasting.Big data research, 14:81–92, 2018","venue":null,"work_id":"864564ba-d327-491f-a622-b0d36ae102f8","year":2018},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9c56f667fbcea10e1221801852efd47720ab96598bca1d2ed9b70bce0e69ee8d","observation_id":"af283600-9ec2-4710-b4fc-9c9691c7c693","resolution":{"observed_at":"2026-07-05T21:11:29.344909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.341890Z","title":"SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.Proceedings","venue":null,"work_id":"4ab3dc3a-1fbb-4d12-853e-38d1eb7931e1","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:559e30478cf2b7335832e6047552c723906bd0a92d15200474687f213229d844","observation_id":"00d4bebd-ce9e-47f3-b394-b0a605874a6f","resolution":{"observed_at":"2026-07-05T21:11:29.343069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.318489Z","title":"A new approach to linear filtering and prediction problems.Transactions of the ASME–Journal of Basic Engineering, 1960","venue":null,"work_id":"81bc2b7f-ea8c-4ea7-8333-f4e199d53475","year":1960},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:c58e17f7931a3ca29a3a10452a30e746e92e5c63f1e66d414e444abf406029c8","observation_id":"5ff5cd60-7c0a-46e8-9ba4-3529815efe47","resolution":{"observed_at":"2026-07-05T21:11:29.319911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.419187Z","title":"Fourth-order time-stepping for stiff PDEs.SIAM Journal on Scientific Computing, 26(4):1214–1233, 2005","venue":null,"work_id":"ed539a94-6654-4a79-8b0b-c90bacf076e9","year":2005},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:c564b7237c9defb7275ed5aa40a24364f6714190ae724d7a1440d9b50bd41a82","observation_id":"de49be03-d00e-46b5-81dd-40d161ec428b","resolution":{"observed_at":"2026-07-05T21:11:29.420594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.415443Z","title":"SIAM, 2016","venue":null,"work_id":"a26155e7-7e6f-4058-874d-ffc47ce1ec2f","year":2016},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:965bbeeb8d27a8629d9f336c315984e2487c393502e1d65ef9abde853777c362","observation_id":"feb44958-097d-46c6-8948-f31c5247ed78","resolution":{"observed_at":"2026-07-05T21:11:29.416836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.413532Z","title":"The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension.Nonlinear Dyn, 102:713–732, 2020","venue":null,"work_id":"1a546576-0140-459a-bd4d-2e78c81006c4","year":2020},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:cc1281aa5e53ae192c07b4e39ae0e2d1bb002f7c2d642359b1441ea3326c75e9","observation_id":"b09fb3c3-bac1-42d8-a367-74508cc58127","resolution":{"observed_at":"2026-07-05T21:11:29.414849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.411609Z","title":null,"venue":null,"work_id":"39fa8e16-744f-47d1-be0c-13ee9e1fd554","year":2017},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:383a4479c8ba81ec1e4c41c68b4f4435fd34c98b63880f2a4994b79184e94b2b","observation_id":"cf28724e-c8d5-4086-8c78-98996419ff37","resolution":{"observed_at":"2026-07-05T21:11:29.412731Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2511.06609","last_updated":"2026-07-15T22:07:40Z","snapshot_observed_at":"2026-08-04T12:59:09.568791Z","submitted_at":"2025-11-10T01:40:35Z","title":"A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series","version":4},"cited_work":{"arxiv_id":"2511.06609","doi":null,"metadata_source":"pith","pith_arxiv_id":"2511.06609","snapshot_observed_at":"2026-07-02T19:27:18.449710Z","title":"A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series","venue":"cs.LG","work_id":"649015e1-47c7-4d1f-9d19-76d5cc72193d","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"cited_paper":"/paper/2511.06609","citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:2bd8fdc601ab723adee2ad926773059daf5dc2614a574dec4e212d400677accd","observation_id":"ab7cd0bc-3a61-4a17-a43b-caf47d17ef8a","resolution":{"observed_at":"2026-07-02T19:27:18.451200Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.429150Z","title":"A survey on long short-term memory networks for time series prediction.Procedia Cirp, 99:650–655, 2021","venue":null,"work_id":"93e352a1-d38c-4923-b3c9-7d13f0207053","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:52d5abcab578a3ea5aaeddca30bf57e759add907af0fbe0dd29aed1df21626ab","observation_id":"388f8b49-ce3c-4ef5-86b1-532752f12664","resolution":{"observed_at":"2026-07-05T21:11:29.430448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.340081Z","title":"On a measure of lack of fit in time series models.Biometrika, 65(2):297–303, 1978","venue":null,"work_id":"d3a81692-38cd-48c6-8023-be8b82c4b498","year":1978},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:3de966707ebfc38d2926aa0f6669be148fb57bc18421d38bc962f9fffe6fafba","observation_id":"51200d18-1505-4903-a362-fa053497aff6","resolution":{"observed_at":"2026-07-05T21:11:29.341367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.417362Z","title":"Hybridnet: integrating model-based and data-driven learning to predict evolution of dynamical systems","venue":null,"work_id":"f7f23a1a-95cc-4609-a401-aa1ab903146b","year":2018},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:c31a740b6d0a650d0a1fe462992831881b553a8cc2a01a2b55b555a2ae9f1bbd","observation_id":"6bac3242-76bf-4c07-90a1-f20b312f5072","resolution":{"observed_at":"2026-07-05T21:11:29.418656Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.439078Z","title":"Deterministic nonperiodic flow 1","venue":null,"work_id":"90e8de98-395a-49dd-ab8f-188fb855b7dc","year":2017},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:50e0f6f3f37825f57cd8094c19413aa992f5b1c713041a47e85ec8e1329bbef0","observation_id":"11270708-1206-423f-9d96-4e8eac41bce7","resolution":{"observed_at":"2026-07-05T21:11:29.440115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.329902Z","title":"Ecological forecasting and data assimilation in a data-rich era.Ecological Applications, 21(5):1429– 1442, 2011","venue":null,"work_id":"9bb61363-3cfe-4bab-8254-bfa2de0e0cdc","year":2011},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:793aacac748b18c32356f61a56e5020a86c26a4d54251cf64bb392c9b7c9b461","observation_id":"d66d3763-9687-49b4-977a-0915fbeb77d9","resolution":{"observed_at":"2026-07-05T21:11:29.331204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.423823Z","title":"Academic press, 1982","venue":null,"work_id":"9a6b3fb7-f022-4881-b89e-dee7a50298e4","year":1982},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:3c300db12145455449fb7550a1680b624d023be69b6c2d30180cc00fd827f7ce","observation_id":"c2fd61b6-7a10-4057-ab81-fb90453c952d","resolution":{"observed_at":"2026-07-05T21:11:29.424927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.316354Z","title":"Weak SINDy for partial differential equations.Journal of Computational Physics, 443:110525, 2021","venue":null,"work_id":"d3ca239d-6bf7-419e-9f7d-8876e221d77c","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:dc1b698ef40359b8d57be722e795ea20a550898a49730cf2750a10d48749e306","observation_id":"b7c4afa5-b5ae-4283-83f4-2afd84caa436","resolution":{"observed_at":"2026-07-05T21:11:29.317951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.378706Z","title":"Weak SINDy: Galerkin-based data-driven model selection.Multiscale Modeling & Simulation, 19(3):1474–1497, 2021","venue":null,"work_id":"a1fd1b6a-87c8-45ab-b5f8-79366065adda","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:b4673ab2074c1a947dbfbef687913e0f6e604722edeea24e00ff9711e75771d6","observation_id":"0f63ecfd-aa18-4829-bd85-7e88c7ebf8f5","resolution":{"observed_at":"2026-07-05T21:11:29.380197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.312023Z","title":"Asymptotic consistency of the WSINDy algorithm in the limit of continuum data.IMA Journal of Numerical Analysis, 45(6):3264–3312, 2025","venue":null,"work_id":"e29892d9-bb5c-4c76-b544-066c2935a3d3","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:761a05490cb16532ee0c5ade554d4bb73b221937bb1cbe7587a7c824be2d0802","observation_id":"5a16cfd5-c1cd-4166-82a8-0ee4923753fe","resolution":{"observed_at":"2026-07-05T21:11:29.313562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.06751","last_updated":"2024-09-10T13:59:17Z","snapshot_observed_at":"2026-08-10T01:40:22.186950Z","submitted_at":"2024-09-10T13:59:17Z","title":"The Weak Form Is Stronger Than You Think","version":1},"cited_work":{"arxiv_id":"2409.06751","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2409.06751","snapshot_observed_at":"2026-07-02T19:27:18.447111Z","title":"arXiv preprint arXiv:2409.06751 , year=","venue":null,"work_id":"f4889879-4f04-44e7-b1d3-533792b20d83","year":2024},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"cited_paper":"/paper/2409.06751","citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:c67655665cdf7fc708456309b31d9c79de9522e935e58d6a2f6cb0fa89dab102","observation_id":"22693dd6-9393-4d23-957d-26bcffb03500","resolution":{"observed_at":"2026-07-02T19:27:18.448529Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.314272Z","title":"On numerical approximations of the Koopman operator.Mathematics, 10(7):1180, 2022","venue":null,"work_id":"61172ce7-cb4b-4570-90eb-8d4793fa42ac","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:cb1f41b91ba6f6d024b6b560287283e37990f6aa7cd29014b41c949926ea064b","observation_id":"ca18880f-b8d5-4e60-9387-299a7f4dc1ab","resolution":{"observed_at":"2026-07-05T21:11:29.315587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.320553Z","title":"Springer","venue":null,"work_id":"721989f8-fa65-4c76-8369-bcd410c43a0e","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9771ed4d9c2b97bc6d47d87f7b3fe46e12c11d4c3714167846483abcc78a891f","observation_id":"7f0f1167-079f-4004-89ce-0cdf88b6c65a","resolution":{"observed_at":"2026-07-05T21:11:29.321775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.436849Z","title":"Data-driven methods for weather forecast","venue":null,"work_id":"23b31a41-24b7-407d-904d-0c43efaf165e","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:118ad34ff4bc0f61d8a8ebd49bd87648112daf4fee174c5aa449d6c9de77729b","observation_id":"ec7c455e-3cc0-479d-9f6b-fc03f4b2c2a1","resolution":{"observed_at":"2026-07-05T21:11:29.438279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.363854Z","title":"A review of data-driven discovery for dynamic systems.International Statistical Review, 91(3):464–492, 2023","venue":null,"work_id":"b3291488-2c3d-41ac-8fbb-c1ecd05585b6","year":2023},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:edd768dbf81a029249f27b05f973c26135c2f785380633e1f57e6c8ef01fb7f4","observation_id":"902131b2-effb-4f94-a45a-54b804fce25c","resolution":{"observed_at":"2026-07-05T21:11:29.365489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2502.09885","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T00:19:13.611941Z","title":"Comprehensive review of neural differential equations for time series analysis, 2025","venue":null,"work_id":"df513caa-182e-4544-b9c9-85303b1eae0e","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:4ff0c0431965e4ba8888c7212ed7726a767cd277be40b789c6bf9923b184add4","observation_id":"581e1322-c3f3-4535-90ce-6dcaa03f69d0","resolution":{"observed_at":"2026-07-02T19:27:18.462063Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.06735","last_updated":"2026-07-02T13:50:00Z","snapshot_observed_at":"2026-08-09T21:01:37.912363Z","submitted_at":"2025-09-08T14:28:23Z","title":"Data-driven discovery of dynamical models in biology","version":2},"cited_work":{"arxiv_id":"2509.06735","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.06735","snapshot_observed_at":"2026-07-03T02:17:06.411511Z","title":"Data-driven discovery of dynamical models in biology.arXiv preprint arXiv:2509.06735, 2025","venue":null,"work_id":"d6e36547-7b45-44b9-8e26-02e0158be221","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"cited_paper":"/paper/2509.06735","citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:f34a0bd86c9ac7c2572e995dd29c2c0779813e1e37c440d1738ac3d4501e79c5","observation_id":"a36d97ab-bf78-48c4-9065-da628d8049b0","resolution":{"observed_at":"2026-07-03T02:17:06.411511Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-07T00:23:12.814709Z","title":"Smoothing and differentiation of data by simplified least squares procedures.Analytical chemistry, 36(8):1627–1639","venue":null,"work_id":"55790df6-fc29-481f-92cd-106b4ac3c8f4","year":1964},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:d6fb1906cfb4743df4baf3373f1d95d98e373bc0ba17c7d7d3d304ea89fbab66","observation_id":"6846d1e0-13a6-43a6-88d7-f231d7bdefea","resolution":{"observed_at":"2026-07-05T21:11:29.453616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2601.06183","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T19:27:18.444190Z","title":"Data-driven reduced-complexity modeling of fluid flows: A community challenge.arXiv preprint arXiv:2601.06183, 2026","venue":null,"work_id":"4f14521b-282a-4ae0-b11f-92c41d2d56b3","year":2026},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:ee40d7703db2e6439106d31e8a2042f5c128fcd92965687ca2edaa167ecb0a99","observation_id":"ae587b34-3d51-4638-990a-0f47d2b45e74","resolution":{"observed_at":"2026-07-02T19:27:18.445927Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.430944Z","title":"Communication in the presence of noise.Proceedings of the IRE, 37(1):10–21, 1949","venue":null,"work_id":"c93adab1-488b-4ea5-82d3-8d80ce854fbf","year":1949},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:83a83e47d2498499b8cd6911ea4af0ec204e24b0b0445dcbf1673dd43575e352","observation_id":"11671967-e294-4e2d-a5a9-d2911bb6ed39","resolution":{"observed_at":"2026-07-05T21:11:29.432186Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.469462Z","title":"Application of dynamic data driven application system in environmental science.Environmental Reviews, 22(3):287–297, 2014","venue":null,"work_id":"f765d08e-9f10-47a7-b11c-fa1adc77523e","year":2014},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:8212e10967878b4000c55dad686bd1652e13d532da33b64b7bc10af654d673c7","observation_id":"4c7534f5-8df3-4a62-958e-335f3434c46e","resolution":{"observed_at":"2026-07-05T21:11:29.470982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.17203","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T19:27:18.457500Z","title":"Learning solution operator of dynamical systems with diffusion maps kernel ridge regression.arXiv preprint arXiv:2512.17203, 2025","venue":null,"work_id":"c17ab58f-78b3-4eb1-bd35-e74f8751385b","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9af6ed8d502306c148117acf16398596d90cd93930fb8faa7489ef149afac69a","observation_id":"ecc7b448-c469-46c7-b729-59eb4a8d6ffc","resolution":{"observed_at":"2026-07-02T19:27:18.459301Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.382877Z","title":"Recent advances in physical reservoir computing: A review","venue":null,"work_id":"6c7a7475-27d2-450c-a8b2-c33e7d9f9695","year":2019},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:d7d02c3597878415c80112112a13ef1140b2e80d01600563ad553a02da279274","observation_id":"40140258-3eb9-4a8f-958b-72fa9d584163","resolution":{"observed_at":"2026-07-05T21:11:29.384391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.442681Z","title":"Sampling-50 years after Shannon.Proceedings of the IEEE, 88(4):569–587, 2002","venue":null,"work_id":"def201ca-90a4-4721-8545-849cd5025bef","year":2002},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:7f1493aaa026380a467a66ce287eb13eed5c8eacbab87153712eff187b4d77d6","observation_id":"562b5d3e-3ec7-4e99-add3-104f680b0067","resolution":{"observed_at":"2026-07-05T21:11:29.443896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.444509Z","title":"A general sampling theory for nonideal acquisition devices.IEEE Transactions on Signal Processing, 42(11):2915–2925, 2002","venue":null,"work_id":"c33d6cce-be6b-4089-b899-9c45530836f9","year":2002},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:7e77a5eef9929b4554d6eb981b0abe63bbb8d9162aadd70a63d6d87faea3afcc","observation_id":"ee60c7a7-0f65-42da-bf79-1995e7b3105e","resolution":{"observed_at":"2026-07-05T21:11:29.445805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.440828Z","title":"Polynomial spline signal approximations: filter design and asymptotic equivalence with Shannon’ s sampling theorem.IEEE Transactions on Information Theory, 38(1):95–103, 2002","venue":null,"work_id":"f6174977-c545-4be7-a1fc-3c724e1d9701","year":2002},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:a4da629b1ec8b7381611497c6c05d73ad1b750e3437ed1d511c93edc1595beee","observation_id":"ae239fd9-8247-4b70-b1ec-42869f012793","resolution":{"observed_at":"2026-07-05T21:11:29.442148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.448289Z","title":"A generalized sampling theory without band-limiting constraints.IEEE transactions on circuits and systems II: analog and digital signal processing, 45(8):959–969, 2002","venue":null,"work_id":"00d252df-986b-409e-860c-1eabdf32915c","year":2002},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:592551d52645640bf197bae7d1682bdb7e70fa2693c8820eee8d919ef93fa9b2","observation_id":"8f004345-1d13-4cd0-829a-64c025db766b","resolution":{"observed_at":"2026-07-05T21:11:29.449651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.461312Z","title":null,"venue":null,"work_id":"ca238719-05a9-41ce-93bc-38c10240ec1d","year":2018},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:db74a51365cb54dd97ad1779b3fccc7a6d5db8d7f0de5994c1a81f70ecdf67b4","observation_id":"6a829b1f-7c3d-48d6-b1a2-f6bae848fad5","resolution":{"observed_at":"2026-07-05T21:11:29.462786Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.459758Z","title":"Kernel ridge regression","venue":null,"work_id":"eaaaf69d-0c8e-4fcb-9a0e-64b204ac465d","year":2013},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:bc3e6ca252be225f4195101202c1c04478a72bec7447ac915d9a48b30b230427","observation_id":"8bd73046-f3a2-48ed-b392-6975169c11cf","resolution":{"observed_at":"2026-07-05T21:11:29.460829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.425478Z","title":"Data-driven neural modeling and chaos control in fractional-order financial dynamical systems.AIP Advances, 16(1), 2026","venue":null,"work_id":"a8054ecc-53b1-4f0c-b071-bcca9358e426","year":2026},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:690f22960a89b94f3ca30b21f670c5d457ede887592cd82b67ca75064acb9ceb","observation_id":"c2f2d233-87d2-41d4-9591-9f6bbdcf3269","resolution":{"observed_at":"2026-07-05T21:11:29.426773Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.427385Z","title":"Gaussian process dynamical models.Advances in neural information processing systems, 18, 2005","venue":null,"work_id":"32d0d58d-f30e-43be-b26e-e67399a212d9","year":2005},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:9d0311410474bfdb81b64bc333938b35ce05bb60085b3257fd6ffcdefa54a8be","observation_id":"70c9a6eb-5044-48f3-a7e5-5cbfc54401dc","resolution":{"observed_at":"2026-07-05T21:11:29.428564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.434831Z","title":"A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition.Journal of Nonlinear Science, 25(6):1307–1346, 2015","venue":null,"work_id":"4e848ad4-774e-4d97-8931-9131a27c3544","year":2015},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:a1a36869b8fa1b40db9ecb9d898cce5e3355386e8ebb8670d69d0973c2365b8a","observation_id":"36a89f5a-0969-4544-86df-60a86a81ef61","resolution":{"observed_at":"2026-07-05T21:11:29.436204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.432744Z","title":"Introduction to ‘communication in the presence of noise’ by CE Shannon","venue":null,"work_id":"fec66e7e-6194-4cc8-bd64-cee141a9d8ea","year":1998},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:367121985401ac94ad4b373828ac3884c634326e08a14a8347f4edd5242bf848","observation_id":"20db2d85-eaa6-4943-8e44-2ffe28413645","resolution":{"observed_at":"2026-07-05T21:11:29.433990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.457984Z","title":"Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology.Physical Biology, 19(6):061001, 2022","venue":null,"work_id":"1aa299fb-97a4-4b88-8623-f54e5ae0e190","year":2022},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:3e62d90f01d821cff69c07ec1e14e2ac6ccc185f67b8795c1ba0245432026ce6","observation_id":"564333ff-0946-496e-8b9c-37357006fc61","resolution":{"observed_at":"2026-07-05T21:11:29.459227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.402413Z","title":"Big data driven mobile traffic understanding and forecasting: A time series approach.IEEE transactions on services computing, 9(5):796–805","venue":null,"work_id":"c14ec21a-0df3-4c63-9ae6-845fd0462d51","year":2016},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:fd256e4a6dd74dbf6b1c478f9336da0c6fec78aa78530cf19bd858c316b56e7c","observation_id":"695da490-8869-436c-bb26-e9bec3cce794","resolution":{"observed_at":"2026-07-05T21:11:29.404225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.349171Z","title":"Emerging opportunities and challenges for the future of reservoir computing.Nature Communications, 15(1):2056, 2024","venue":null,"work_id":"83c1eaba-3ffd-4573-a932-638a727d8ec6","year":2056},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:09d393447d69dd0c21cd0774973688994b66465676e3d8b46e17df41243abe1a","observation_id":"b0753c26-7ee5-4f2b-a892-3aa708b586c5","resolution":{"observed_at":"2026-07-05T21:11:29.350488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.347271Z","title":"Gaussian process for long-term time-series forecasting","venue":null,"work_id":"d84337bf-ac45-40ce-850d-05bbc0a91156","year":2009},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:de21eb869b8476fc83dcc5deca0b30a23fb66f314b3f1e83909dc78c2ed26ec5","observation_id":"57506876-5398-4a0c-a576-0a45d0699066","resolution":{"observed_at":"2026-07-05T21:11:29.348601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.350997Z","title":"Inference of dynamic systems from noisy and sparse data via manifold-constrained gaussian processes.Proceedings of the National Academy of Sciences, 118(15):e2020397118, 2021","venue":null,"work_id":"7cb04682-4947-4067-8146-0229b8f0f65f","year":2021},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:bdecee584c2e63f2e2453404b0d2f45195f44b15cb1ad4a6673d9bd8b71a0bbe","observation_id":"e7c05632-87d5-4182-87ff-be6e396e1ed5","resolution":{"observed_at":"2026-07-05T21:11:29.352237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.357375Z","title":"Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling","venue":null,"work_id":"8624d68a-6a64-4b67-8925-d9ed923b0474","year":2015},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:2fc0ede5889191598c2722e4b0dfa6396789d6a6504a9882312ba446165c10ce","observation_id":"622affc6-9cf4-4f18-823a-998996b0006f","resolution":{"observed_at":"2026-07-05T21:11:29.358855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.361792Z","title":"Learning networked dynamical system models with weak form and graph neural networks.Journal of Guidance Control and Dynamics, 2026","venue":null,"work_id":"edbf0c40-9e20-4bae-a563-5113cb01f7ee","year":2026},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:1b27edcb5e3591326ab9bd84c866ee453d32bbfd2bf7f314ba4cf9fdf914e4cb","observation_id":"210a0ae4-8977-462e-bdca-1e63433936d8","resolution":{"observed_at":"2026-07-05T21:11:29.363191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.353014Z","title":"A review of recurrent neural networks: LSTM cells and network architectures.Neural computation, 31(7):1235–1270, 2019","venue":null,"work_id":"8f91cd51-b447-431d-9fd5-46914cc19714","year":2019},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:79f93cea72658a07a1a75e90f7fbf340d5b69c675ffa23604aa3453e70c53614","observation_id":"42440d2a-5092-40b0-8a5e-b2713090248a","resolution":{"observed_at":"2026-07-05T21:11:29.354372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.387263Z","title":"On the convergence of the SINDy algorithm.Multiscale Modeling & Simulation, 17(3):948–972, 2019","venue":null,"work_id":"9bb68c6a-45f8-4b8a-a883-5c071bfe8b26","year":2019},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:62e98042330e6592c82ac0e64e3ef74f1560465c1eb33077e9540f5240b9bd06","observation_id":"e0ee9bbc-0077-46c2-be24-46178a3b4128","resolution":{"observed_at":"2026-07-05T21:11:29.388762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-05T21:11:29.391231Z","title":"Accelerating neural ODEs: a variational formulation-based approach","venue":null,"work_id":"9f0b9e6c-039a-4cca-b773-115827b0103e","year":2025},"citing_paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-07-02T19:26:59.341194Z"},"links":{"citing_paper":"/paper/2607.00257"},"observation_digest":"sha256:211559faeef760bc3d3c741a8ed6f8a76680699242b7679cfeaf32d909e65025","observation_id":"ac608fb1-eec0-4045-a1d2-eed22aac20d0","resolution":{"observed_at":"2026-07-05T21:11:29.392602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.00257","last_updated":"2026-06-30T23:07:55Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T22:46:59.765362Z","submitted_at":"2026-06-30T23:07:55Z","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression"},"reference_resolution":{"displayed":86,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":3,"verified_exact":6,"verified_fuzzy":76},"total_outbound_references":86},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 86 of 86 outbound references and 0 inbound Pith citation observations for arXiv:2607.00257."}