{"as_of":"2026-08-14T09:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6e41d6de2a75ebdf54d18190b0da1f1794ceffb82161f8d107317d11fb6caba8","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:13:16.666626Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2501.09395/citation-record","integrity":"/paper/2501.09395/integrity","json":"/paper/2501.09395/citation-record.json","paper":"/paper/2501.09395"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.540447Z","title":"Physics- informed machine learning","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.540447Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:fef39588e0ad6cc1c25bf3a202822501d8571140e0db07d6cac0cda2c5313965","observation_id":"94a05eea-0465-44c1-9428-6968d00f2e22","resolution":{"observed_at":"2026-08-10T20:13:16.540447Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:17.067903Z","title":"Tackling the curse of dimensionality with physics-informed neural networks","venue":null,"work_id":"df30a34d-157e-4ad7-9fc2-6c9428978351","year":2024},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.546208Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:f909fcc8c44f3d9fae5bcf74fe0d5bdf1371174f91422508745223e17830c369","observation_id":"13c561e5-7566-4ba6-9af3-be0bb1c5b40b","resolution":{"observed_at":"2026-08-10T20:13:17.073300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:17.048217Z","title":"Dgm: A deep learning algorithm for solving partial differential equations","venue":null,"work_id":"1c28ad8b-322b-4d5e-92b4-1f806fbbc99b","year":2018},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.551793Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:931bed0f69cebdaa68b2ad58dd64197511ddc2a59b9954b6efcc612ad591bdcb","observation_id":"a17e0c25-de10-4f5a-ac35-378feae5b90b","resolution":{"observed_at":"2026-08-10T20:13:17.053529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:17.030601Z","title":"The deep minimizing movement scheme","venue":null,"work_id":"0be56d11-b08d-4612-bc12-c60f940d5252","year":2023},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.557095Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:69ea2caeaf83d0b26f8157a8a42805c312221b1f09a1de382fb2bfbe578713a1","observation_id":"11d4477f-e0b5-40b2-9c73-d577cd0d561f","resolution":{"observed_at":"2026-08-10T20:13:17.036483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.562842Z","title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.562842Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:64c10b765fafbc42233c954ab36163f9aa54ab593b41a9f5222a582ba38c8ed5","observation_id":"3798c2d4-abfa-4c2b-a7c9-388ca361c73d","resolution":{"observed_at":"2026-08-10T20:13:16.562842Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.568122Z","title":"Deepxde: A deep learning library for solving differential equations","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.568122Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:4d8f2c7e9fcc15e4d1a006eab1c1e7edef049a5e2015933eeb58ce7287935c54","observation_id":"61afb082-be15-46f0-9a21-6d680e3d7d33","resolution":{"observed_at":"2026-08-10T20:13:16.568122Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.573993Z","title":"Physics-informed neural networks (pinns) for fluid mechanics: A review","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.573993Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:081e48ee067209666edfd279166f11004cd9d18fe33d28b46b74e390461d7084","observation_id":"e8635b76-159f-408c-9517-c50f5b75d488","resolution":{"observed_at":"2026-08-10T20:13:16.573993Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.972129Z","title":"Deep neural network approach to forward-inverse problems","venue":null,"work_id":"e02f8f52-4eb8-4a36-8584-1f8d3f5aec30","year":2020},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.578882Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:45a3128bffb29ca927b32aca86025c415df754807a677ef68b0e333775179925","observation_id":"c828679b-a123-4ee9-a9dd-c3721168caa5","resolution":{"observed_at":"2026-08-10T20:13:16.977389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:16.953934Z","title":"A pinn approach for identifying governing parameters of noisy thermoacoustic systems","venue":null,"work_id":"38ddc9dc-8789-48f8-97ac-217450f46304","year":2024},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.584261Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:7e4450be10ff80e36bf56814946479d5749e65abe5b029d4164c5ba6912eaad8","observation_id":"78a2f59b-a2ba-4449-86ce-be8d78b6d6f8","resolution":{"observed_at":"2026-08-10T20:13:16.959473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.589689Z","title":"Learning nonlinear operators via deeponet based on the universal approximation theorem of operators","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.589689Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:4b41678923b4632097fa222fa7a381be1bc3675e36661d5b40e4bcb103f41801","observation_id":"32780854-f65f-4446-a3b7-a9128f1e9bcf","resolution":{"observed_at":"2026-08-10T20:13:16.589689Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.595592Z","title":"Neural operator: Learning maps between function spaces with applications to pdes","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.595592Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:0eedcafff69ee409666904102c2cd4576648c772e0347180bc5c79cd3a2f52fa","observation_id":"30fca564-9fbe-4050-9b2c-dc922d5e95bc","resolution":{"observed_at":"2026-08-10T20:13:16.595592Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-08-13T05:47:30.530742Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-10T20:13:16.601136Z","title":"Fourier neural operator for parametric partial differential equations","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.601136Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:49232066f325d71fc2b62f2a468f44328af7335ce66e34e7f754e7513bec4857","observation_id":"0b75c4ed-0c11-447d-a8c8-10788a5e834a","resolution":{"observed_at":"2026-08-10T20:13:16.601136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.606742Z","title":"Learning the solution operator of parametric partial differential equations with physics-informed deeponets","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.606742Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:f5140a69af69a2a06418bebe3778174927fa96a601772433d496113a6f74bfc1","observation_id":"3e878a1b-1991-44ca-ad02-560ff2a89c6a","resolution":{"observed_at":"2026-08-10T20:13:16.606742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.03161","last_updated":"2025-02-07T09:56:51Z","snapshot_observed_at":"2026-08-12T14:34:27.393034Z","submitted_at":"2024-12-04T09:38:58Z","title":"Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.03161","snapshot_observed_at":"2026-08-10T20:13:16.611531Z","title":"Physics-informed deep inverse operator networks for solving pde inverse problems","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.611531Z"},"links":{"cited_paper":"/paper/2412.03161","citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:36eb0b80f6453d01a5dceae5c42e234a1adb6e09835b10d6b006c653dd89cf4a","observation_id":"42f88179-814b-4ae4-abe2-ba35198223c6","resolution":{"observed_at":"2026-08-10T20:13:16.611531Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.11404","last_updated":"2022-05-23T15:47:47Z","snapshot_observed_at":"2026-08-13T15:38:45.695533Z","submitted_at":"2022-05-23T15:47:47Z","title":"Variable-Input Deep Operator Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.11404","snapshot_observed_at":"2026-08-10T20:13:16.616780Z","title":"Variable-input deep operator networks","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.616780Z"},"links":{"cited_paper":"/paper/2205.11404","citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:1444c6a4a3293536c71dc0061e5bf9c7c68d2bb523fe896a96794165f89741b9","observation_id":"8eb56b76-458e-4497-bdda-0b95115e585c","resolution":{"observed_at":"2026-08-10T20:13:16.616780Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.04690","last_updated":"2025-02-19T09:47:56Z","snapshot_observed_at":"2026-08-13T10:38:12.897032Z","submitted_at":"2023-08-09T03:56:07Z","title":"Finite Element Operator Network for Solving Elliptic-type parametric PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.04690","snapshot_observed_at":"2026-08-10T20:13:16.622083Z","title":"Finite element operator network for solving parametric pdes","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.622083Z"},"links":{"cited_paper":"/paper/2308.04690","citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:1c5fd957de4910b8feb4c092c66a6277fd978a23c59ceefeae24b607766e6632","observation_id":"454ba1fa-11de-4513-a776-22fadf61498a","resolution":{"observed_at":"2026-08-10T20:13:16.622083Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.899747Z","title":"Unsupervised legendre–galerkin neural network for solving partial differential equations","venue":null,"work_id":"376d3e2e-58e9-471c-b1fd-fb82e99078e3","year":2023},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.627166Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:fccd103a7b7bd02e52831e5b4c55a09414b901b3c846685b235ebcdcd6d59383","observation_id":"5b86bcb7-61d4-43a3-8e08-2fa616430de9","resolution":{"observed_at":"2026-08-10T20:13:16.905667Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:16.882497Z","title":"Universal approximation using incremental constructive feedforward networks with random hidden nodes","venue":null,"work_id":"491bafe8-4784-433d-8674-09356df22893","year":2006},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.631988Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:4997a1f405e7ff024056a81e356ae1bc4e47ff25ad74a693fa4eba676b04be84","observation_id":"17d80aa1-7073-4f4b-a77c-f9168ccec5c3","resolution":{"observed_at":"2026-08-10T20:13:16.888319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:16.865159Z","title":"Extreme learning machine and its applications","venue":null,"work_id":"3bea9943-a080-43b2-a270-d0669ecbdf96","year":2014},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.636928Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:90abe62f37e1510ef866b9aedab715456fe4a097828112d7e9b965a0154f10d7","observation_id":"11ba2996-4cbc-4121-baa5-7b08cfc3d4c5","resolution":{"observed_at":"2026-08-10T20:13:16.871209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:16.848221Z","title":"Trends in extreme learning machines: A review","venue":null,"work_id":"8209b1b1-4477-4ff2-8ead-0382f3f5d1db","year":2015},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.641747Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:a3ef926f89cb2dcb6f1c692387e67acff0c5661e90262d598595d0db18ca47aa","observation_id":"0a2df36b-f9c4-4f03-a14d-c11d4abe5139","resolution":{"observed_at":"2026-08-10T20:13:16.853416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T20:13:16.831243Z","title":"A review on extreme learning machine","venue":null,"work_id":"ba0f5000-24f4-4222-831e-8586a5454c2b","year":2022},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.646787Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:b52ca3e136289c8c89da767aabb4f395ff42d4e547035ef282f6a75dce69c07d","observation_id":"3cd654e2-0975-43b0-8915-3b1e8ea0120d","resolution":{"observed_at":"2026-08-10T20:13:16.836462Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.651517Z","title":"Physics informed extreme learning machine (pielm)–a rapid method for the numerical solution of partial differential equations","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.651517Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:dab01a6b8223b7890c06a77bf52b6f46734aa200f4db7ad60b9a23243f91999c","observation_id":"989c1d9b-e944-4676-85a9-560070d308d4","resolution":{"observed_at":"2026-08-10T20:13:16.651517Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.803044Z","title":"Augmented physics informed extreme learning machine to solve the biharmonic equations via fourier expansions","venue":null,"work_id":"a29c7c53-b0cc-44cd-b6ac-d9490d21b39b","year":null},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.656339Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:1e23ae96325a2b0f67554178ca64c08ffded56d377c709c3b7094c99671e9b42","observation_id":"b0ef2e3c-a667-474e-89c4-0c9b63b02f44","resolution":{"observed_at":"2026-08-10T20:13:16.808530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-10T20:13:16.661591Z","title":"Adam: A method for stochastic optimization","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.661591Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:df12beb9c984e35ae41746711c0183173671678f9ef35f183e948ada0fa46109","observation_id":"8dce53d2-657a-45c8-acaa-d13f792e9473","resolution":{"observed_at":"2026-08-10T20:13:16.661591Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:13:16.783574Z","title":"On stability and regularization for data-driven solution of parabolic inverse source problems","venue":null,"work_id":"89412d07-69a7-476f-8420-2c4f2df57796","year":2023},"citing_paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:13:16.666626Z"},"links":{"citing_paper":"/paper/2501.09395"},"observation_digest":"sha256:bb765a171f118631a9964eff0e8b7050f7bd43083311a07a4527a0ffdbb4afea","observation_id":"4cc65f44-baf4-42f2-9c5e-301bc2b39f4e","resolution":{"observed_at":"2026-08-10T20:13:16.790964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.09395","last_updated":"2025-01-16T09:06:43Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-12T02:50:27.919869Z","submitted_at":"2025-01-16T09:06:43Z","title":"ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":0,"verified_fuzzy":12},"total_outbound_references":25},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2501.09395."}