{"as_of":"2026-08-14T08:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f37dd013e6b06f8c073ea7c12ebf18f5115ac94dac3d3f9f7f74b6c8e58da0c9","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:14:00.176704Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"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/2412.00636/citation-record","integrity":"/paper/2412.00636/integrity","json":"/paper/2412.00636/citation-record.json","paper":"/paper/2412.00636"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:14:00.439848Z","title":"The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems","venue":null,"work_id":"f22618eb-cc4e-44cc-bce7-7a286bd36579","year":2018},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.092080Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:3916344a950d63ea51d404161d0eb696a622e97fe14f0dce9df062558daced68","observation_id":"84c6ad7f-d668-4c0d-8732-536f38535e98","resolution":{"observed_at":"2026-08-12T05:14:00.442742Z","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":"2026-08-12T05:14:00.432424Z","title":"Karniadakis","venue":null,"work_id":"27e8614f-3830-40b7-b6db-b6dc14781aeb","year":2019},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.095370Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:7c62a4f041435b2c0e443c05ff3e0af2bb66776b1662ca6e689b5edf9473600b","observation_id":"33505817-c324-4afc-b516-3c2fcb721d95","resolution":{"observed_at":"2026-08-12T05:14:00.435154Z","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":"2026-08-12T05:14:00.098845Z","title":"DGM: A deep learning algorithm for solving partial differential equations","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.098845Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:e705b86c4c28bafd82d1ae83e32d4e381a0cf1365582db4dc806212cf9dac854","observation_id":"8af38cf2-1e3b-4cd4-b9e1-92e48a08b1fc","resolution":{"observed_at":"2026-08-12T05:14:00.098845Z","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":"2026-08-12T05:14:00.420063Z","title":"Physics- informed neural networks (PINNs) for fluid mechanics: A review","venue":null,"work_id":"d58f7c16-d1ff-4ce0-9f4c-a0dea80ab5df","year":2021},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.101673Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:abc35c858cf5a595cddc7ff6f6387e3734a540226bd13ce93c85b7f5228f5b70","observation_id":"17afc991-bbc1-4587-9a64-a37427fecdd6","resolution":{"observed_at":"2026-08-12T05:14:00.423840Z","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":"2026-08-12T05:14:00.412387Z","title":"Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence","venue":null,"work_id":"ae59aa55-f0f5-489d-9331-e23935d31d8a","year":2019},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.104500Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:26fa2214cdf5957ba0a50a117866d1744820887dedace60b1081354c09d77e63","observation_id":"0310b854-7273-4b09-bca4-5abe35e2a48d","resolution":{"observed_at":"2026-08-12T05:14:00.415557Z","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":"2026-08-12T05:14:00.404940Z","title":"Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence","venue":null,"work_id":"6cfb49df-2a70-4096-a0ad-eeb9edf89fef","year":2020},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.108579Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:673fac8b55ce4904d29afb82b5abe5140314f9ece40c2a5edf4e3de832b7b58a","observation_id":"afb8c50d-9706-44c7-8e53-6effddd3a5f6","resolution":{"observed_at":"2026-08-12T05:14:00.407762Z","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":"2026-08-12T05:14:00.397453Z","title":"A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems","venue":null,"work_id":"17fdf2ba-c927-4f90-b061-e76388b89a02","year":2020},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.112173Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:1e07155d650c5853eb7bada7e184a2c7066e3acfc4852371f3a606c9a4b8b0e2","observation_id":"e33c79c3-4813-47b2-8ded-2763611433e9","resolution":{"observed_at":"2026-08-12T05:14:00.400452Z","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":"2026-08-12T05:14:00.115206Z","title":"fPINNs: Fractional physics-informed neural networks","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.115206Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:19d887541fe2df9b4e4cb979fb8541447e83c2fd255a84f052f07d3baca64320","observation_id":"84d2b865-5676-496b-928d-decb4dd37c9e","resolution":{"observed_at":"2026-08-12T05:14:00.115206Z","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":"2026-08-12T05:14:00.384574Z","title":"A comprehensive study of non- adaptive and residual-based adaptive sampling for physics-informed neural networks","venue":null,"work_id":"317a99b6-d263-49d4-bbcb-c7feb0362dc9","year":2023},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.117747Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:a9535610958064239ab46d8a1e35782fa670d8b9ef6f0ff1de6d0eaa373a3cf1","observation_id":"bca8fd9b-b613-4b40-8a95-1e970fa8396c","resolution":{"observed_at":"2026-08-12T05:14:00.388482Z","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":"2026-08-12T05:14:00.377025Z","title":"Failure-informed adaptive sampling for PINNs","venue":null,"work_id":"ca78227f-c2c5-45f2-bf46-0dbe3ba13403","year":2023},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.120243Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:41a8f75430cf3fcb4715eae12656379c9816042cca5b72060dbdb1d0e3fbce6e","observation_id":"cec19f1c-3085-4d9c-a637-b94085f7e841","resolution":{"observed_at":"2026-08-12T05:14:00.379810Z","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":"2026-08-12T05:14:00.368650Z","title":"Failure-informed adaptive sampling for PINNs, part II: combining with re-sampling and subset simulation.Communications on Applied Mathematics and Computation, 6(3):1720–1741, 2024","venue":null,"work_id":"6018b211-6e60-45ac-9c75-4d5dbb33e252","year":2024},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.122625Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:0ed593242acdced656629ce87a250b6fd3b1d50197898df9bc5142ac2a91269f","observation_id":"399fb36a-3279-428e-8ce9-bef82e70aa86","resolution":{"observed_at":"2026-08-12T05:14:00.371939Z","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":"2026-08-12T05:14:00.360432Z","title":"Jagtap, Kenji Kawaguchi, and George Em Karniadakis","venue":null,"work_id":"30285931-19c8-4cb2-82a1-e109dd27eb57","year":2020},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.124931Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:0caae4d6f86c821e7fb07842b7b2bafda34642c3af70cdea1632f4a96ef80870","observation_id":"fd61def2-18b9-4ead-a708-010cbe0616ca","resolution":{"observed_at":"2026-08-12T05:14:00.363315Z","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":"2026-08-12T05:14:00.352209Z","title":"Jagtap, Kenji Kawaguchi, and George Em Karniadakis","venue":null,"work_id":"d3b46c49-df8d-4e47-83bf-2c70f60ab31b","year":2020},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.127299Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:c1c82b451a1327127628b573fd475f79432c5f8a7852d757e8d9dd823ced2ba1","observation_id":"97e35151-6ac9-48e6-b8e1-f53b4effc863","resolution":{"observed_at":"2026-08-12T05:14:00.355700Z","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":"2026-08-12T05:14:00.343996Z","title":"Self-adaptive physics-informed neural networks using a soft attention mechanism","venue":null,"work_id":"412e12d0-98a6-4229-a826-4436083252dd","year":2023},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.129858Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:ff5f2cf3cf82ba510bfe691afd57188dc26e28812b034e955b72ff33f20b1378","observation_id":"4e0d48e5-5e35-47fc-b9c7-a338435b032a","resolution":{"observed_at":"2026-08-12T05:14:00.347103Z","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":"2026-08-12T05:14:00.132406Z","title":"Self-adaptive loss balanced physics-informed neural networks","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.132406Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:e37d8c49037e6ffbbf87a875aa5f773edfe64e72b9d50a75cf722493a69407d1","observation_id":"ad0f3431-3e72-4915-ad5c-003c9eeb976e","resolution":{"observed_at":"2026-08-12T05:14:00.132406Z","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":"2026-08-12T05:14:00.331200Z","title":"Taylor, Manuela Bastidas, Victor M","venue":null,"work_id":"2a7f03ee-e9b9-4383-8b45-e5ae73de2c38","year":2024},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.134749Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:32ef534a6f92799bc0bbd9dbf291461c47a8e0d82b75dbc8bb027164a4309947","observation_id":"524c74bd-463f-421d-bc82-747131a7308a","resolution":{"observed_at":"2026-08-12T05:14:00.334047Z","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":"2026-08-12T05:14:00.323652Z","title":"Self-adaptive deep neural network: Numerical approx- imation to functions and PDEs","venue":null,"work_id":"b89d7cb2-8343-4e59-b8aa-870de761ddcf","year":2022},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.137208Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:2ef9c6ff63a9ea1b15df7b5926c4f7ba2abb2c81bf807595fb461b9320ea7f61","observation_id":"83032b9e-20a8-4878-b7bf-1737cb8bd18f","resolution":{"observed_at":"2026-08-12T05:14:00.326433Z","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":"2026-08-12T05:14:00.314802Z","title":"Adaptive two-layer ReLU neural network: II","venue":null,"work_id":"9abe37dd-b788-4e6e-a21a-1e2bb08af8f0","year":2022},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.139468Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:7f0e9382d965569a55508f92e52530de074e09d75540c7ffb15d4de5aea78e2f","observation_id":"606d2370-7409-4221-8df2-10e151323a66","resolution":{"observed_at":"2026-08-12T05:14:00.317997Z","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":"2026-08-12T05:14:00.307006Z","title":"Adaptive two-layer relu neural network: I","venue":null,"work_id":"08e62c37-52f4-40f8-9f40-1e6dfe8c6c53","year":2022},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.141827Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:5fca6b40cf2d2faeca322008e2e0cf5d0f877fe5a990743efaf06257735e533e","observation_id":"b3fe7065-cac8-464a-a0c4-7ff92940a404","resolution":{"observed_at":"2026-08-12T05:14:00.309786Z","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":"2026-08-12T05:14:00.144350Z","title":"Kingma and Jimmy Lei Ba","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.144350Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:51b556070685ee500c27d02fceba8c9c59561b75e0f977472806a0b745824981","observation_id":"884abd94-ca2f-43e9-85fb-56b2d5f326ed","resolution":{"observed_at":"2026-08-12T05:14:00.144350Z","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":"2026-08-12T05:14:00.298124Z","title":"Influence of activation functions on the convergence of physics-informed neural networks for 1d wave equation","venue":null,"work_id":"e190153f-3bd9-4780-937d-56f0a67e2661","year":2023},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.146725Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:8a8d43786634276fb59f37917408b7110e861c183e95556cd2263680fc3bffd4","observation_id":"51b9d628-9167-4517-b6a7-dcc20e86de05","resolution":{"observed_at":"2026-08-12T05:14:00.301174Z","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":"2026-08-12T05:14:00.289013Z","title":"On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition","venue":null,"work_id":"5dbbac09-8f8b-4b17-b9cf-aea10da9dd01","year":1957},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.149230Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:9da20f74145967b4f6adfd4c70a94f8a67653d4df900fe58141ed479d5962928","observation_id":"085af41e-cc76-41db-a89c-b3fc57d6678a","resolution":{"observed_at":"2026-08-12T05:14:00.292033Z","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":"2026-08-12T05:14:00.280205Z","title":null,"venue":null,"work_id":"e210cc7c-1932-4ef4-b696-1de18245a08d","year":1962},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.152326Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:2e74393ef14e060f38fb93934ee7c836706ed3cd197054bf4a591c970252bfe1","observation_id":"bbd2a334-47dc-4f9c-888f-72bd8b447c08","resolution":{"observed_at":"2026-08-12T05:14:00.283583Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-12T05:14:00.272148Z","title":null,"venue":null,"work_id":"40971b00-7a43-49fe-8a25-7ae0f7068583","year":1966},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.155744Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:c0789c8e317430976ed156361e8d9838f6d1b914b717e567a6bd4e66cf670dbe","observation_id":"65379fba-a866-48c5-8ffc-877e2c9bb17f","resolution":{"observed_at":"2026-08-12T05:14:00.275738Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-12T05:14:00.264352Z","title":"Sprecher and Sorin Draghici","venue":null,"work_id":"fea02aaa-10ed-4749-b07b-fa1e196a790e","year":2002},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.158185Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:b5bf902261bde4ca2e45b1b511a316ff8c84fed7acbf3a27a0ada51a8f861601","observation_id":"cbd8336e-f2ac-4d2e-97ff-35a80a56e2f1","resolution":{"observed_at":"2026-08-12T05:14:00.267771Z","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":"2026-08-12T05:14:00.257141Z","title":"The kolmogorov superposition theorem can break the curse of dimensionality when approximating high dimensional functions","venue":null,"work_id":"0357565a-295e-4136-8806-cecc8bdff5ed","year":2023},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.160601Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:33196f7b6f912d565900f5281060fce82cab201332f1af19b9c850a78830abf1","observation_id":"23d80adc-b749-4f49-8411-86d6935dd7de","resolution":{"observed_at":"2026-08-12T05:14:00.260046Z","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":"2026-08-12T05:14:00.248697Z","title":"Kolmogorov’s theorem and multilayer neural networks","venue":null,"work_id":"77ec9e21-70fb-498e-b31e-f2d51116c7d6","year":1992},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.163121Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:beebc6c5dfaaf388bc6bdc28404066d58357b8af79531d46c21336ad220fe508","observation_id":"d9416839-e69f-4b41-b561-6ebae82c2552","resolution":{"observed_at":"2026-08-12T05:14:00.251877Z","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":"2026-08-12T05:14:00.238773Z","title":"The kolmogorov-arnold representation theorem revisited","venue":null,"work_id":"76e0ce50-55e5-404d-9d36-596f591bb088","year":2021},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.165615Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:b080599fcd289162cb685cbf5e44328cb26dec6b22c94c62eb8231d0d8f0b64a","observation_id":"a923ab15-9879-4276-9157-849d4ce0e274","resolution":{"observed_at":"2026-08-12T05:14:00.242117Z","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":"2026-08-12T05:14:00.229942Z","title":"A kol- mogorov high order deep neural network for high frequency partial differential equations in high dimensions","venue":null,"work_id":"b8d2541c-b07f-4919-92da-a32098b70f4d","year":2024},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.168756Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:6d2a56170ba452161396505665ce1ba74bef3d4defcbf8ddacf6c0843c84d477","observation_id":"c14512f0-edc8-4a94-9236-7d5277ffd3f1","resolution":{"observed_at":"2026-08-12T05:14:00.233437Z","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":"2026-08-12T05:14:00.221138Z","title":"Selected topics in finite element methods","venue":null,"work_id":"472e42f5-7528-4b45-8300-ef99f5454018","year":2010},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.171523Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:3534fff9666f9e72c0f634a6482c3d93efe6279ebf5cf4283afb63a088c56a06","observation_id":"91d4b469-5d3b-4566-9ef1-5e7f267f200a","resolution":{"observed_at":"2026-08-12T05:14:00.224542Z","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":"2026-08-12T05:14:00.211735Z","title":"DBSCAN: Density-based spatial clustering of appli- cations with noise","venue":null,"work_id":"2812851f-1cf2-43c8-96ca-941eab3dfccd","year":2012},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.174268Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:811d2285204b0eb1f012360e74a9520328f622b5d311c64bead0941b80ccd4f1","observation_id":"48c37e45-78e9-4f77-8977-1f09ee1d2f79","resolution":{"observed_at":"2026-08-12T05:14:00.215146Z","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":"2026-08-12T05:14:00.201977Z","title":"Moving sampling physics-informed neural networks induced by moving mesh PDE","venue":null,"work_id":"208cfeda-4531-4b8a-bae5-7b7da5942edc","year":2024},"citing_paper":{"arxiv_id":"2412.00636","last_updated":"2024-12-01T01:23:42Z","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T05:14:00.176704Z"},"links":{"citing_paper":"/paper/2412.00636"},"observation_digest":"sha256:1e390c08a241d7125b824bbd468ead740831078d8d553b28190618e91fc52fde","observation_id":"1ab55524-5d5a-47b7-9a29-9a91a76cfa3c","resolution":{"observed_at":"2026-08-12T05:14:00.206433Z","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":"2412.00636","last_updated":"2024-12-01T01:23:42Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-14T07:02:00.595804Z","submitted_at":"2024-12-01T01:23:42Z","title":"Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":0,"verified_fuzzy":26},"total_outbound_references":32},"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 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2412.00636."}