{"as_of":"2026-08-19T08:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dba24bb087ae31e0220a4c56ca8dcdb67665db8d1bc013868239d57ceb15fb0c","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":55,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:16:43.717139Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":79,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2305.14703","last_updated":"2026-04-17T20:21:10Z","snapshot_observed_at":"2026-08-13T08:46:51.338633Z","submitted_at":"2023-05-24T04:15:34Z","title":"Generative diffusion learning for parametric partial differential equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-24T09:06:10.327568Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2305.14703"},"observation_digest":"sha256:0e2d244b2d30005ba9b85363429f7fe48bc772e653301332aba34ce39abca155","observation_id":"e72c7a0d-9d01-426e-a4f8-c48d40eaea2a","resolution":{"observed_at":"2026-05-24T09:09:15.695837Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2407.00809","last_updated":"2026-06-02T21:20:03Z","snapshot_observed_at":"2026-08-16T13:38:20.799434Z","submitted_at":"2024-06-30T19:28:12Z","title":"Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-23T23:08:36.689122Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2407.00809"},"observation_digest":"sha256:f08b9f44c1af2e787613d8770f01e81d285aaf47df1f66678f3120abecf87380","observation_id":"0ae81296-4958-4e52-ab45-b4575f810be2","resolution":{"observed_at":"2026-05-23T23:13:37.081139Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-12T10:37:31.595120Z","title":"Neural operator: Learning maps between function spaces,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.19125","last_updated":"2024-11-28T13:16:20Z","snapshot_observed_at":"2026-08-16T18:13:45.224281Z","submitted_at":"2024-11-28T13:16:20Z","title":"Advancing Generalization in PINNs through Latent-Space Representations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T10:37:31.595120Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2411.19125"},"observation_digest":"sha256:7d8a36107450970fe64ed20eec514eb7b0470c4e3062404037099874f9be9974","observation_id":"3bcbb5d1-32fa-456a-81ba-1d3f3ad22bcc","resolution":{"observed_at":"2026-08-12T10:37:31.595120Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-11T21:31:32.080748Z","title":"Kovachki et al","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.04409","last_updated":"2025-05-05T09:50:28Z","snapshot_observed_at":"2026-08-14T13:34:22.673023Z","submitted_at":"2024-12-05T18:31:14Z","title":"Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T21:31:32.080748Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2412.04409"},"observation_digest":"sha256:5d30d63f71c6edf0a8f5b2a011bce493b00598d8011d1a6c8f95b152cc5084b3","observation_id":"9af83b0a-018f-43e2-986f-bc49ee875bbd","resolution":{"observed_at":"2026-08-11T21:31:32.080748Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-11T20:00:50.158237Z","title":"URLhttps://proceedings.mlr.press/v37/ioffe15.html","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.06195","last_updated":"2024-12-09T04:25:37Z","snapshot_observed_at":"2026-08-18T00:13:34.193275Z","submitted_at":"2024-12-09T04:25:37Z","title":"Adaptive Resolution Residual Networks -- Generalizing Across Resolutions Easily and Efficiently","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-11T20:00:50.158237Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2412.06195"},"observation_digest":"sha256:8102ecc08d9912336dec71025a4fbec43706ea409db15fe8a92ea517ff4bc846","observation_id":"dbb2abc2-cbba-4af5-93b1-d0641bdd2e65","resolution":{"observed_at":"2026-08-11T20:00:50.158237Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-11T17:56:26.529541Z","title":"Kovachki , author Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.08426","last_updated":"2024-12-11T14:47:19Z","snapshot_observed_at":"2026-08-16T00:22:21.278595Z","submitted_at":"2024-12-11T14:47:19Z","title":"Koopman Theory-Inspired Method for Learning Time Advancement Operators in Unstable Flame Front Evolution","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T17:56:26.529541Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2412.08426"},"observation_digest":"sha256:b9f6d5ae7279a8336c8789482b9b463c67c3c6a2efc025f054fa93be19d1e658","observation_id":"022cdcf7-5d4c-405f-ab67-0d833b50a5af","resolution":{"observed_at":"2026-08-11T17:56:26.529541Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-11T17:28:16.265450Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.09009","last_updated":"2025-05-14T08:00:18Z","snapshot_observed_at":"2026-08-18T12:30:34.548500Z","submitted_at":"2024-12-12T07:22:02Z","title":"A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems","version":4},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-11T17:28:16.265450Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2412.09009"},"observation_digest":"sha256:f35eb0ab141c568cc93d1f31460fa1161d863685047ea3e3d5cd4a0d7cd85d78","observation_id":"ca6d54ee-50f3-48de-b1a4-36af8321f55c","resolution":{"observed_at":"2026-08-11T17:28:16.265450Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-10T22:19:37.455186Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.02379","last_updated":"2025-05-30T21:08:32Z","snapshot_observed_at":"2026-08-15T11:56:12.258668Z","submitted_at":"2025-01-04T20:51:51Z","title":"TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T22:19:37.455186Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2501.02379"},"observation_digest":"sha256:c7b220e0c233c0843e9c10f1f10d6107e865fa378a74d0c4b26369eb2f86e845","observation_id":"f4527fda-9936-4a61-8d42-5af7c9106887","resolution":{"observed_at":"2026-08-10T22:19:37.455186Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-10T15:03:35.664232Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.14636","last_updated":"2025-01-24T16:55:36Z","snapshot_observed_at":"2026-08-16T10:14:32.426016Z","submitted_at":"2025-01-24T16:55:36Z","title":"A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T15:03:35.664232Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2501.14636"},"observation_digest":"sha256:7bc7bd281073f1f37477ab0b66866e3be3987f5e15b7ea6430077a848ea30df0","observation_id":"b53941da-edbb-4826-84e0-c33fcb165f85","resolution":{"observed_at":"2026-08-10T15:03:35.664232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-09T13:05:20.262521Z","title":"URL:http://arxiv.org/abs/2108.08481, doi:10.5555/3648699.3648788","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.02195","last_updated":"2025-07-09T10:59:52Z","snapshot_observed_at":"2026-08-18T08:54:55.793774Z","submitted_at":"2025-02-04T10:21:14Z","title":"EFKAN: A KAN-Integrated Neural Operator For Efficient Magnetotelluric Forward Modeling","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T13:05:20.262521Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2502.02195"},"observation_digest":"sha256:17b28dd7bded53442be2705f4984105fb8fd83f32731648c7130d9f5d9fdcd8e","observation_id":"e8aae612-adde-4ce8-a308-090c11a8cc9e","resolution":{"observed_at":"2026-08-09T13:05:20.262521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-08T05:46:28.133504Z","title":"Neural operator: Learning maps between function spaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.08683","last_updated":"2025-02-12T11:16:15Z","snapshot_observed_at":"2026-08-17T01:10:55.854154Z","submitted_at":"2025-02-12T11:16:15Z","title":"A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T05:46:28.133504Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2502.08683"},"observation_digest":"sha256:984f42fc08823df3e835dedc01603f19629bc27396f4eb37f21bca7a52f9c276","observation_id":"7cab24c7-16be-49bc-9f95-99cf82168681","resolution":{"observed_at":"2026-08-08T05:46:28.133504Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T19:43:57.768053Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.10033","last_updated":"2025-02-14T09:23:13Z","snapshot_observed_at":"2026-08-17T11:05:48.562781Z","submitted_at":"2025-02-14T09:23:13Z","title":"Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T19:43:57.768053Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2502.10033"},"observation_digest":"sha256:189855ae461722a82671879da06162b6c6df0d0e4865a7c263951d9654a7858f","observation_id":"dfbca8f4-6bc6-4071-9c2e-12703dbca6e0","resolution":{"observed_at":"2026-08-07T19:43:57.768053Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2503.14568","last_updated":"2025-03-18T11:19:08Z","snapshot_observed_at":"2026-08-15T02:00:44.746666Z","submitted_at":"2025-03-18T11:19:08Z","title":"Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-05-22T23:51:39.466995Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2503.14568"},"observation_digest":"sha256:3a556b6624691600290029d0f9c790f6c068517429b4c82feec835b13e142925","observation_id":"acbca17f-c801-41da-9363-28ec9c5468e0","resolution":{"observed_at":"2026-05-22T23:52:16.918861Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-16T05:16:43.717139Z","title":"[Kurakin et al., 2017] Alexey Kurakin, Ian Goodfellow, and Samy Bengio","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21155","last_updated":"2025-05-01T04:26:16Z","snapshot_observed_at":"2026-08-19T05:44:56.437956Z","submitted_at":"2025-04-29T20:17:43Z","title":"Evaluation and Verification of Physics-Informed Neural Models of the Grad-Shafranov Equation","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T05:16:43.717139Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2504.21155"},"observation_digest":"sha256:11969a1756d40eff6b9268f44f2e818323b5aaad620b9eca70ae1a68074d50c4","observation_id":"2c1fae0a-5d92-4743-99f3-69b6e3ad2c74","resolution":{"observed_at":"2026-08-16T05:16:43.717139Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-15T21:03:00.463755Z","title":"Neural operator: Learning maps between function spaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.11157","last_updated":"2025-05-16T11:59:30Z","snapshot_observed_at":"2026-08-18T21:52:06.630553Z","submitted_at":"2025-05-16T11:59:30Z","title":"Attention on the Sphere","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T21:03:00.463755Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2505.11157"},"observation_digest":"sha256:7e6c9b745cc5d5f198976b2a4ad0a34802a1dc9a777ca2c8e5d95f22e9f23c8b","observation_id":"5e674294-43e8-4f83-b0d6-46903f950a2a","resolution":{"observed_at":"2026-08-15T21:03:00.463755Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T14:58:38.018328Z","title":"Neural Operator : Learning Maps Between Function Spaces , May 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.16996","last_updated":"2025-05-22T17:56:38Z","snapshot_observed_at":"2026-08-17T09:41:32.447041Z","submitted_at":"2025-05-22T17:56:38Z","title":"A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T14:58:38.018328Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2505.16996"},"observation_digest":"sha256:74df5bd60ea65c4711fe437670f8a5332a96e2c5f05613b40cae49a2c2686d45","observation_id":"453965a8-81c8-44cf-be95-625fdf05be59","resolution":{"observed_at":"2026-08-07T14:58:38.018328Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T14:24:44.047914Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.19105","last_updated":"2025-05-28T07:11:21Z","snapshot_observed_at":"2026-08-18T11:05:10.485105Z","submitted_at":"2025-05-25T11:51:31Z","title":"Latent Mamba Operator for Partial Differential Equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T14:24:44.047914Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2505.19105"},"observation_digest":"sha256:1a5c31915011a1e83683b3e4969c45512ab8e62b1d9ac386d6c6f9619d137f0a","observation_id":"95b9b567-a5ad-49dd-82f2-e8c218a29413","resolution":{"observed_at":"2026-08-07T14:24:44.047914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T06:01:41.912814Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.06623","last_updated":"2025-09-09T02:29:24Z","snapshot_observed_at":"2026-08-09T18:35:29.236001Z","submitted_at":"2025-06-07T01:57:08Z","title":"Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-07T06:01:41.912814Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.06623"},"observation_digest":"sha256:402a1c5a10f5ff2f17d4709fb85720697896f688d6b49d1b64fea3a4c3fb9fd7","observation_id":"54e62085-dc27-4f66-acea-0011bc21ed95","resolution":{"observed_at":"2026-08-07T06:01:41.912814Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T05:23:49.111356Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.08226","last_updated":"2025-06-09T20:52:04Z","snapshot_observed_at":"2026-08-14T03:28:21.539921Z","submitted_at":"2025-06-09T20:52:04Z","title":"Mondrian: Transformer Operators via Domain Decomposition","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:23:49.111356Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.08226"},"observation_digest":"sha256:4d1738d79d51f1f5d11c495f698a50055958111afd0825b97df2b89a3a7d3fde","observation_id":"e5c31bbc-cb84-4d4c-bd11-e1cc523fddc2","resolution":{"observed_at":"2026-08-07T05:23:49.111356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2506.14665","last_updated":"2026-04-21T17:59:57Z","snapshot_observed_at":"2026-08-17T10:57:13.534794Z","submitted_at":"2025-06-17T15:56:56Z","title":"Accurate and scalable exchange-correlation with deep learning","version":6},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-19T09:06:01.804744Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.14665"},"observation_digest":"sha256:d175f2908783b1edb6002520e0601a36f7b86a78e3c5653c82b53d3c81f7d697","observation_id":"73678889-47ce-4b6e-8979-01cbe0406b2d","resolution":{"observed_at":"2026-05-19T09:07:13.947633Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-15T19:52:08.596078Z","title":"Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.15199","last_updated":"2026-07-05T11:48:06Z","snapshot_observed_at":"2026-08-19T07:11:47.342129Z","submitted_at":"2025-06-18T07:25:09Z","title":"Interpretability and Generalization Bounds for Learning Spatial Physics","version":4},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T19:52:08.596078Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.15199"},"observation_digest":"sha256:54314ee2407024db65489d2c2e404393ca7a9d9ac2510fc91e774e227efa5d7f","observation_id":"d656cb1b-b07d-4310-82e4-59a8b3ea925f","resolution":{"observed_at":"2026-08-15T19:52:08.596078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T21:26:34.338031Z","title":"Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-17T13:53:35.629254Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.338031Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:8b2f8d388a4e509fe88c126ae8df57383c10fb7aecddfb53fe91699faa3d4659","observation_id":"1b4e4631-634c-431a-842d-0a1d3ee9410c","resolution":{"observed_at":"2026-08-06T21:26:34.338031Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T19:27:46.639151Z","title":"arXiv preprint arXiv:2108.08481 (2021)","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05584","last_updated":"2025-07-08T01:43:33Z","snapshot_observed_at":"2026-08-09T18:36:01.999651Z","submitted_at":"2025-07-08T01:43:33Z","title":"The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:27:46.639151Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.05584"},"observation_digest":"sha256:0300f317de7917d7e4180968fc80ae0c7381a647afa8e17ec9388ef00e9adf6b","observation_id":"ec2973c2-c63c-4f23-9b75-8f9b6b9383ce","resolution":{"observed_at":"2026-08-06T19:27:46.639151Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2507.15774","last_updated":"2026-05-14T16:58:20Z","snapshot_observed_at":"2026-08-12T18:27:06.012431Z","submitted_at":"2025-07-21T16:29:29Z","title":"Time Series Forecasting Through the Lens of Dynamics","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-19T03:31:48.513830Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.15774"},"observation_digest":"sha256:25a450f0edf32344cafe5e2085ad5928ccab4cab26a44d7a62be271551a952e1","observation_id":"f8f7839d-69f0-40d9-8b1c-623ea2dbd3a6","resolution":{"observed_at":"2026-05-19T03:32:01.331749Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T13:02:54.464045Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.21244","last_updated":"2025-07-28T18:02:57Z","snapshot_observed_at":"2026-08-13T18:22:05.194068Z","submitted_at":"2025-07-28T18:02:57Z","title":"Bubbleformer: Forecasting Boiling with Transformers","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T13:02:54.464045Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.21244"},"observation_digest":"sha256:a15402e2180b407cfc901bc4d34f287b36ce3b569ae520cc78d5b06361d3487a","observation_id":"fb6952aa-d2cb-4603-aeb7-5aadff637db4","resolution":{"observed_at":"2026-08-06T13:02:54.464045Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T11:54:56.893686Z","title":"Neural operator: Learning maps between function spaces,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.22301","last_updated":"2025-07-30T00:24:17Z","snapshot_observed_at":"2026-08-14T01:02:06.020771Z","submitted_at":"2025-07-30T00:24:17Z","title":"Toward Intelligent Electronic-Photonic Design Automation for Large-Scale Photonic Integrated Circuits: from Device Inverse Design to Physical Layout Generation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T11:54:56.893686Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.22301"},"observation_digest":"sha256:66025a1a7966c7323ec66ebf8f4be38518c93fe22b27aa57d41c0374a37df23e","observation_id":"017054dd-9e09-4ec1-9fee-928057c78a5e","resolution":{"observed_at":"2026-08-06T11:54:56.893686Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T16:16:13.303354Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.18806","last_updated":"2025-08-26T08:40:42Z","snapshot_observed_at":"2026-08-18T23:19:17.602927Z","submitted_at":"2025-08-26T08:40:42Z","title":"Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-05T16:16:13.303354Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2508.18806"},"observation_digest":"sha256:a2e38bd4ead5c4cadd754841542afd8ca45612539845000988c2205e61c068af","observation_id":"d5771126-6644-43fc-86bd-7a27543f2f80","resolution":{"observed_at":"2026-08-05T16:16:13.303354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-15T16:49:49.725383Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.20650","last_updated":"2026-08-02T03:02:52Z","snapshot_observed_at":"2026-08-17T23:06:52.891880Z","submitted_at":"2025-08-28T10:53:00Z","title":"Self-composing neural operators for high-frequency and multiscale PDE surrogates","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T16:49:49.725383Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2508.20650"},"observation_digest":"sha256:5c806aa08f4989d722c746756f35b886f728c72f3565ee9e467fde11d3b3ce74","observation_id":"9159519a-5644-4fd8-bab6-a157bd1eba12","resolution":{"observed_at":"2026-08-15T16:49:49.725383Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T17:57:20.298639Z","title":"Neural Operator: Learning Maps Between Function Spaces, April 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2026-08-09T19:01:33Z","snapshot_observed_at":"2026-08-16T11:59:12.982703Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.298639Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:becc7c7b5910e8b46bac9e3f9183a6fab2c1e028ed23f115703bd566b29bbf80","observation_id":"70de1d89-488e-413b-9b55-ae4160e23cfc","resolution":{"observed_at":"2026-08-04T17:57:20.298639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T18:00:37.393578Z","title":"B., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10384","last_updated":"2025-09-12T16:18:16Z","snapshot_observed_at":"2026-08-13T12:57:51.443540Z","submitted_at":"2025-09-12T16:18:16Z","title":"Flow Straight and Fast in Hilbert Space: Functional Rectified Flow","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T18:00:37.393578Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2509.10384"},"observation_digest":"sha256:d17a6eccb6dbf9fa0154f4ce0301afb2deb670fba7fa6ab7426c83122b45ed0c","observation_id":"d1e7a98a-a8c9-440d-a8da-dc8925ea71c5","resolution":{"observed_at":"2026-08-04T18:00:37.393578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2511.22112","last_updated":"2025-11-27T05:05:29Z","snapshot_observed_at":"2026-08-12T14:21:52.819590Z","submitted_at":"2025-11-27T05:05:29Z","title":"Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-17T04:28:07.806965Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2511.22112"},"observation_digest":"sha256:420a4920dd8eb2f3c8d2aa18f43f608ae7bf081de0f956c9b996df601fe97617","observation_id":"0bc7f050-cf83-4141-83c4-65c0cfcbbfce","resolution":{"observed_at":"2026-05-17T04:29:01.577905Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-03T10:03:08.114701Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.11428","last_updated":"2026-05-22T18:30:16Z","snapshot_observed_at":"2026-08-09T18:36:17.094202Z","submitted_at":"2026-01-16T16:47:44Z","title":"Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families","version":7},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T10:03:08.114701Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2601.11428"},"observation_digest":"sha256:f73610b8e2236b04bf6e9f0b5c90db3c16078d3baa8adc62393f427ad7194624","observation_id":"089473c7-acdf-48d8-8017-b2c163fc9a93","resolution":{"observed_at":"2026-08-03T10:03:08.114701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-03T08:39:53.658327Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.17074","last_updated":"2026-07-27T14:35:04Z","snapshot_observed_at":"2026-08-11T20:09:02.796005Z","submitted_at":"2026-01-23T00:43:51Z","title":"Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation","version":5},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-03T08:39:53.658327Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2601.17074"},"observation_digest":"sha256:455e6748ec610683af47087c5db9c2c36b394246e9d71445be72ca1c7e1488b9","observation_id":"770e2f02-32e8-47e6-81c6-f30b2ed725a7","resolution":{"observed_at":"2026-08-03T08:39:53.658327Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T17:47:08.876587Z","title":"Nikola B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.28791","last_updated":"2026-07-22T20:51:41Z","snapshot_observed_at":"2026-08-15T19:40:44.118393Z","submitted_at":"2026-03-21T23:14:13Z","title":"Learning 3D Hypersonic Flow with Physics-Enhanced Neural Fields: A Case Study on the Orion Reentry Capsule","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-02T17:47:08.876587Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2603.28791"},"observation_digest":"sha256:a9ff252666afec1d7a6ece3cfb780f9e7eceae0b66af137334e51007f5bb7af4","observation_id":"6f14a7d7-4e29-43c5-a9a1-6025b4e9ea56","resolution":{"observed_at":"2026-08-02T17:47:08.876587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.17922","last_updated":"2026-04-20T07:59:22Z","snapshot_observed_at":"2026-08-15T01:42:49.044816Z","submitted_at":"2026-04-20T07:59:22Z","title":"Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-10T04:32:48.021389Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.17922"},"observation_digest":"sha256:f78c28e105a3d76622e22883cd8f2571dfe6ac8a7c6ababbd838778e542a0a13","observation_id":"4bb34af7-2d61-4b35-a07d-30fbc1d9da79","resolution":{"observed_at":"2026-05-11T11:51:02.887767Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.25985","last_updated":"2026-04-28T17:08:25Z","snapshot_observed_at":"2026-08-18T21:50:39.095415Z","submitted_at":"2026-04-28T17:08:25Z","title":"Learning Neural Operator Surrogates for the Black Hole Accretion Code","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-07T15:28:38.494462Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.25985"},"observation_digest":"sha256:f66aad69d28319d96e6e49b2beb88a3ba7dc0d29d1745de552c0d69fe6f60b34","observation_id":"db4d474d-4d4a-4a05-a4ba-92c2bb20e277","resolution":{"observed_at":"2026-05-12T00:21:23.706098Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.26621","last_updated":"2026-04-29T12:46:00Z","snapshot_observed_at":"2026-08-11T09:27:06.490560Z","submitted_at":"2026-04-29T12:46:00Z","title":"Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-07T10:58:07.460227Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.26621"},"observation_digest":"sha256:28ea7507a767591cd6b6f05c4fe6044f0b6d5410a06b9bedfa2a6fc2f1bc7187","observation_id":"ab798e1b-4da5-49a8-a430-01c00b4238ff","resolution":{"observed_at":"2026-05-09T04:00:13.226916Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.27158","last_updated":"2026-04-29T20:04:20Z","snapshot_observed_at":"2026-08-16T20:40:47.300222Z","submitted_at":"2026-04-29T20:04:20Z","title":"Hybrid Fourier Neural Operator-Lattice Boltzmann Method","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-07T08:13:46.567661Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.27158"},"observation_digest":"sha256:1165b29f1b6e63a0475e9ae62fb1ac09156d5d191e4518cac21c3b2ea05e493c","observation_id":"9a352f99-0b3f-43c7-a269-373f17867da5","resolution":{"observed_at":"2026-05-12T10:01:29.191030Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.07738","last_updated":"2026-05-08T13:46:28Z","snapshot_observed_at":"2026-08-12T19:11:10.352533Z","submitted_at":"2026-05-08T13:46:28Z","title":"Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-11T03:02:47.843748Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.07738"},"observation_digest":"sha256:e0472680a13ec8c7fd6ea8db9d55437c5f5c246c3acf64a052cd2cc9c84b69c6","observation_id":"a7563a6a-68f8-4a24-8e23-9792fd5b8799","resolution":{"observed_at":"2026-05-11T03:05:52.639855Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.08170","last_updated":"2026-08-02T06:51:30Z","snapshot_observed_at":"2026-08-11T15:08:50.265631Z","submitted_at":"2026-05-04T22:15:21Z","title":"Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-12T01:38:54.274354Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.08170"},"observation_digest":"sha256:b7d31467e49bdf4f8fe3dd04e8e66074598450745563207aef63b35cfd583bff","observation_id":"0577a301-314c-4ce4-a2e2-ed27a03db1d1","resolution":{"observed_at":"2026-05-12T01:46:14.665992Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T05:24:02.533981Z","title":"Neural operator: Learning maps between function spaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.08170","last_updated":"2026-08-02T06:51:30Z","snapshot_observed_at":"2026-08-11T15:08:50.265631Z","submitted_at":"2026-05-04T22:15:21Z","title":"Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T05:24:02.533981Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.08170"},"observation_digest":"sha256:052e04a7e0d9cc99bc667b555ad1f8a4b6558d03041f6dcfabb15ec5e64eebb7","observation_id":"b2825f0b-305f-4db1-ae0e-709b9d9f7a9b","resolution":{"observed_at":"2026-08-04T05:24:02.533981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.28909","last_updated":"2026-05-27T17:18:39Z","snapshot_observed_at":"2026-08-12T19:12:01.793601Z","submitted_at":"2026-05-27T17:18:39Z","title":"Sequential Physics-Constrained Neural Operator Forward Modeling for the $\\textit{Norne}$ Reservoir System","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-29T14:37:05.393813Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.28909"},"observation_digest":"sha256:5632b4075f76112289b0f001c0811daaee81c8debf5a673cdaa98af23bf8bf1a","observation_id":"8020b2c7-0eff-4682-828a-8711f7e8e7c7","resolution":{"observed_at":"2026-06-29T14:43:30.814908Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.08654","last_updated":"2026-06-07T14:49:37Z","snapshot_observed_at":"2026-08-14T18:40:47.930323Z","submitted_at":"2026-06-07T14:49:37Z","title":"Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T18:39:56.578189Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.08654"},"observation_digest":"sha256:25128d04369db2700f061656ae0a4c2fc763dec7e709947a41aba33a0319864d","observation_id":"8a1d67db-173e-42a4-99b6-1a409fb035ed","resolution":{"observed_at":"2026-07-02T22:47:25.734752Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.09432","last_updated":"2026-06-08T12:42:10Z","snapshot_observed_at":"2026-07-06T23:48:48.962930Z","submitted_at":"2026-06-08T12:42:10Z","title":"Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-06-27T17:07:27.417845Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.09432"},"observation_digest":"sha256:4249f3e957bf9a5ff0ed7457e935336b19441f49c58951ff1055a88f373ccdb4","observation_id":"7a68dcee-5982-4e44-9b3a-625f89151e7b","resolution":{"observed_at":"2026-07-03T00:37:29.962633Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.20771","last_updated":"2026-06-18T15:38:20Z","snapshot_observed_at":"2026-08-13T08:46:55.474402Z","submitted_at":"2026-06-18T15:38:20Z","title":"ELADO: Elliptic PDE Assessment Datasets for Operator Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T18:20:00.248849Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.20771"},"observation_digest":"sha256:404bd54f6da76fe3823140207a9bee7d3501394d2fed69b172d9e46a123e08c5","observation_id":"83867a57-49bb-49a1-9e83-f420380419a3","resolution":{"observed_at":"2026-07-04T03:09:30.476831Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.25259","last_updated":"2026-06-24T00:34:53Z","snapshot_observed_at":"2026-08-14T11:52:28.582165Z","submitted_at":"2026-06-24T00:34:53Z","title":"A Neural Surrogate Approach for Simulating Natural Convection Problems","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-06-25T20:40:24.100365Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.25259"},"observation_digest":"sha256:3168dc31fae969f774d91c274bf41b3cfde8be4e64c155b494586f39d1286a36","observation_id":"32be2990-fc75-4d23-8324-235d9fbcf085","resolution":{"observed_at":"2026-06-25T21:18:24.265402Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T07:10:15.668361Z","title":"Journal of Machine Learning Research 24, 1–97","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13074","last_updated":"2026-07-12T20:04:39Z","snapshot_observed_at":"2026-08-16T02:03:10.495192Z","submitted_at":"2026-07-12T20:04:39Z","title":"When is the combined load identifiable from a stress-intensity profile? A coupled forward-inverse study on SIFBench finite-element data","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T07:10:15.668361Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.13074"},"observation_digest":"sha256:80079f4d4b6c601865dc4c590a6ef31941ba7abd7be78482dd5aa908fb74f67b","observation_id":"31970c1b-1e79-4d27-b105-ec6fecf51f0f","resolution":{"observed_at":"2026-08-02T07:10:15.668361Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T02:17:07.159977Z","title":"Neural operator: Learning maps between function spaces with applications to PDEs,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14394","last_updated":"2026-07-15T22:17:25Z","snapshot_observed_at":"2026-08-19T07:25:06.208950Z","submitted_at":"2026-07-15T22:17:25Z","title":"DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T02:17:07.159977Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.14394"},"observation_digest":"sha256:4cd0e71497abf7a6a92fdea24aba8a02de6ae01c59fc26556cb0d2e1d0c9a36a","observation_id":"45037c94-c6cc-423f-978c-df46b14d5e62","resolution":{"observed_at":"2026-08-02T02:17:07.159977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-01T06:09:01.761928Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22004","last_updated":"2026-07-24T06:07:14Z","snapshot_observed_at":"2026-08-17T22:16:48.205416Z","submitted_at":"2026-07-24T06:07:14Z","title":"Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers","version":1},"reference_index":2001,"source":"pdf_text","source_observed_at":"2026-08-01T06:09:01.761928Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.22004"},"observation_digest":"sha256:f97470a6aba5e0f531ffa4b6ecf7ff701e3049f4babe6b154de8517fc4a0171d","observation_id":"eeb4939a-a03e-4a91-aa8c-d7e2a6accdfa","resolution":{"observed_at":"2026-08-01T06:09:01.761928Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-07-31T01:28:50.733155Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25100","last_updated":"2026-07-27T21:58:13Z","snapshot_observed_at":"2026-08-13T03:01:27.628936Z","submitted_at":"2026-07-27T21:58:13Z","title":"Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-31T01:28:50.733155Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.25100"},"observation_digest":"sha256:7661febafcee9cfa7c8b1048ace2a2cc73dd5798e2c3499c8b3c2bb825663045","observation_id":"54143cd1-341d-4100-b70c-ec769592ed0a","resolution":{"observed_at":"2026-07-31T01:28:50.733155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-07-31T02:27:17.167700Z","title":"arXiv e-prints , keywords =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28604","last_updated":"2026-07-30T17:54:43Z","snapshot_observed_at":"2026-08-06T11:18:05.221988Z","submitted_at":"2026-07-30T17:54:43Z","title":"Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-07-31T02:27:17.167700Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.28604"},"observation_digest":"sha256:91def8a334bb7ae67768b7276d73e8a8542a1169cdec08925d943d6aca0ad616","observation_id":"e069b584-2f4c-412b-9f3b-8ac1dfa9087a","resolution":{"observed_at":"2026-07-31T02:27:17.167700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T19:54:15.550167Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.01839","last_updated":"2026-08-03T07:49:27Z","snapshot_observed_at":"2026-08-13T17:18:11.160883Z","submitted_at":"2026-08-03T07:49:27Z","title":"tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T19:54:15.550167Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.01839"},"observation_digest":"sha256:552b9034b082e67d85e35785b485133707aded7ca57fef08afd562d70f16f052","observation_id":"9718d6a2-f21b-40e5-87f6-3695857158d9","resolution":{"observed_at":"2026-08-04T19:54:15.550167Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T18:32:35.100763Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04708","last_updated":"2026-08-05T11:19:21Z","snapshot_observed_at":"2026-08-18T11:39:29.312592Z","submitted_at":"2026-08-05T11:19:21Z","title":"Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:32:35.100763Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.04708"},"observation_digest":"sha256:70bb463f3f0d6c90e1d1b14de52d8b56584cf7f677abe0b5080d9425ffd91dc4","observation_id":"1f007116-23d8-4c08-a1a2-75621fd337ac","resolution":{"observed_at":"2026-08-06T18:32:35.100763Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-12T05:35:48.116758Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.11134","last_updated":"2026-08-11T16:53:36Z","snapshot_observed_at":"2026-08-15T22:10:58.000579Z","submitted_at":"2026-08-11T16:53:36Z","title":"Mastering Stochastic OLG Models in Continuous Time","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-12T05:35:48.116758Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.11134"},"observation_digest":"sha256:e3decf50238cd261e66a17a9ed7893ce8daf94da2ff572003ea6e1088f97a1e0","observation_id":"41d836ee-1708-495d-9538-f9adfc50cb99","resolution":{"observed_at":"2026-08-12T05:35:48.116758Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-14T05:59:43.887535Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.13490","last_updated":"2026-08-13T17:18:25Z","snapshot_observed_at":"2026-08-19T02:42:52.874863Z","submitted_at":"2026-08-13T17:18:25Z","title":"DD-RNO: A Domain-Decomposed Routed Neural Operator for Airfoil Flow Prediction","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T05:59:43.887535Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.13490"},"observation_digest":"sha256:1fbd244264eac1479a500329fda1b12527e13f478c0c6bd847b63c32a49070dc","observation_id":"8c0fd9da-dca5-47db-8cae-9f21f8f81011","resolution":{"observed_at":"2026-08-14T05:59:43.887535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2108.08481/citation-record","integrity":"/paper/2108.08481/integrity","json":"/paper/2108.08481/citation-record.json","paper":"/paper/2108.08481"},"outbound":[],"paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","latest_version":6,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-18T00:27:31.145577Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 55 inbound Pith citation observations for arXiv:2108.08481."}