{"as_of":"2026-08-23T12:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c7568d44eec6180bb38b782d3c462850bb4f8b21672f5c693e048fb2f6945870","coverage":[{"denominator":61,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":61,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:13:11.111534Z","state":"measured"},{"denominator":61,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":61,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2504.21328/citation-record","integrity":"/paper/2504.21328/integrity","json":"/paper/2504.21328/citation-record.json","paper":"/paper/2504.21328"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.895467Z","title":"Lee \\ and\\ author I","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.895467Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f1b99a2390817011cf281defe9775ebd1b3aaffd44891f0f2363c6e78cb2a541","observation_id":"7610bc05-582f-4b34-9466-538a18acd3fb","resolution":{"observed_at":"2026-08-16T05:13:10.895467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.899676Z","title":"Meade \\ and\\ author A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.899676Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:68637ad5e0cdda93ced402fc239aaf49c649542556c5fe8544272fcbf15499ee","observation_id":"e68643de-6e63-403b-a7bc-9afefb91b48c","resolution":{"observed_at":"2026-08-16T05:13:10.899676Z","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":"2026-08-16T05:13:12.672183Z","title":"Perdikaris P","venue":null,"work_id":"7435f5e9-4bfb-4d11-9507-ac00a66a8387","year":2019},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.903807Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:a34a5d153b4297e8402c2690d29ed4444d31ff3f352651196e137261de85ab31","observation_id":"a1976555-a5f0-4bf3-9436-8175a1e09967","resolution":{"observed_at":"2026-08-16T05:13:12.675642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1711.10561","last_updated":"2017-11-28T21:21:59Z","snapshot_observed_at":"2026-08-15T08:52:31.204350Z","submitted_at":"2017-11-28T21:21:59Z","title":"Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.10561","snapshot_observed_at":"2026-08-16T05:13:10.907427Z","title":"Raissi , author P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.907427Z"},"links":{"cited_paper":"/paper/1711.10561","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:cc64a8954c56ee88c2a7a42a35a07122242e9b80cd1c7f7ed1b9d1424c755a28","observation_id":"f4a86d95-a909-435d-aea0-fac763e7362c","resolution":{"observed_at":"2026-08-16T05:13:10.907427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.10566","last_updated":"2017-11-28T21:29:35Z","snapshot_observed_at":"2026-08-18T12:17:52.664650Z","submitted_at":"2017-11-28T21:29:35Z","title":"Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.10566","snapshot_observed_at":"2026-08-16T05:13:10.912250Z","title":"Raissi , author P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.912250Z"},"links":{"cited_paper":"/paper/1711.10566","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:03eed8c29277c120eb2609d40eff0a9296e6dadd71e154c2d9a03623e5de0183","observation_id":"2e5a3dbb-15b8-4f3f-929c-b58a58e74125","resolution":{"observed_at":"2026-08-16T05:13:10.912250Z","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":"2026-08-16T05:13:12.661597Z","title":null,"venue":null,"work_id":"2699d436-c90b-46e7-be4a-4e21110ecbbd","year":2018},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.916465Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:4b14a5d03b0578958578513204928bf4145cfe984441553f27b2a8aecd88510c","observation_id":"9def4f8c-f817-40c5-8ccd-f82612487919","resolution":{"observed_at":"2026-08-16T05:13:12.665052Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.651212Z","title":null,"venue":null,"work_id":"424e5466-e220-4c44-8c7e-b61c7cbb070f","year":2011},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.920274Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:0a4ddeb093b41709c524cb763725f794c24485431421b6624d3854bb0391e650","observation_id":"865c94b4-2618-4068-ae7b-351465916b53","resolution":{"observed_at":"2026-08-16T05:13:12.654621Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.640844Z","title":null,"venue":null,"work_id":"ecd61dc6-48fb-4be3-af8e-3be3159b9569","year":2016},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.924154Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:df9c93c63727978dfcfa8cbe0083ed563560f9ffe5c1d5dc13ded892e96dbf9b","observation_id":"b625c46d-521b-44df-9f6e-08f629ed8137","resolution":{"observed_at":"2026-08-16T05:13:12.644443Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:10.928050Z","title":"Jeong , author J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.928050Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:c984b106f26e2fe6cf6677a603e04612bc726e335ca9e510dfab4bde2884e924","observation_id":"b654f34e-5339-44a3-81c3-6ca6a54c8b0b","resolution":{"observed_at":"2026-08-16T05:13:10.928050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.931873Z","title":"Kervadec , author J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.931873Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:61661b2e58723fd37a08d2f347725125d227dc68d4bd088fcba3ec65041cc501","observation_id":"1c808cde-eed9-4e7d-a6c1-df4834c740d8","resolution":{"observed_at":"2026-08-16T05:13:10.931873Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.935642Z","title":"\\ Chiu , author J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.935642Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:00a3e5eb4952239f0cadf0335f1d296190a8c39e912a15a464fab65f55a74468","observation_id":"b75ba7b5-0186-487d-bc81-970fb316be97","resolution":{"observed_at":"2026-08-16T05:13:10.935642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.939177Z","title":"Zhang , author Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.939177Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:ac208a099316000f376481666bff6895a0dadef364b089d330678d41be284e31","observation_id":"5c28cb6d-c9e1-43c5-9439-c8ebb7ddb2ec","resolution":{"observed_at":"2026-08-16T05:13:10.939177Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.942927Z","title":"Sharma , author W","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.942927Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:3540f85e446c04f4f5dcf857c5b27284d8f2825553a3a7639fb0f5cfd0c9e5a9","observation_id":"1f31c51f-b656-4635-a1b5-f9d67f70b17d","resolution":{"observed_at":"2026-08-16T05:13:10.942927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.947037Z","title":"Pang , author L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.947037Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f7c043e3aeac56f7925deaf879c3d0a877ab833166b65f8fad9700a2dc744919","observation_id":"2617979f-5387-471b-a5d1-fb15abb00e4c","resolution":{"observed_at":"2026-08-16T05:13:10.947037Z","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":"2026-08-16T05:13:12.630414Z","title":"\\ Liao \\ and\\ author C.-A","venue":null,"work_id":"242f9a70-8e67-4e01-995c-974fbe172d0e","year":2021},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.950690Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:43469892df99387613964399d3dc7ab00381b2cc2028b75aa29019fbecb4f009","observation_id":"84c5e273-547c-4cd4-8939-d74479f19d11","resolution":{"observed_at":"2026-08-16T05:13:12.634179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:10.953992Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.953992Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:ed34774c9d15af9e5aa2a7150bc6e23f0d3c3606d6875806f0bee392b153c3aa","observation_id":"71538ab0-c25f-47b6-93ef-c595b37ecb08","resolution":{"observed_at":"2026-08-16T05:13:10.953992Z","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":"2026-08-16T05:13:12.619530Z","title":null,"venue":null,"work_id":"1864bb93-d6ae-4d29-93be-8935f138dac0","year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.958200Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:9e7d538ccede60ae57131b5708a9007c03c9c9f1614c3d2acdee15f3a4967a7f","observation_id":"8658dc64-e3cf-4d72-9d3d-57c22ce3bfaf","resolution":{"observed_at":"2026-08-16T05:13:12.623327Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:10.961635Z","title":"Sirignano , author J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.961635Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:482539d499368c3cd4555d9260d1d2f2002c7f4cb53acab59c56d321a93b70d8","observation_id":"9f63a0d7-f9d5-442c-b90d-aee266fa875a","resolution":{"observed_at":"2026-08-16T05:13:10.961635Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.965426Z","title":"Kochkov , author J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.965426Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:b4a2353afbedf301547040870ee16f778870ed701ef55c636d9203232cc3fe21","observation_id":"9561bcd2-1553-4946-8f63-5a9b69f2bbd2","resolution":{"observed_at":"2026-08-16T05:13:10.965426Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.968897Z","title":"Maulik , author O","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.968897Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:53e4b817efc9625dd0f23b8299bdb65be8239ff913a4c9296b7aa7d63bf3858a","observation_id":"b9567b0a-faac-4660-9255-b183bd5cbdd8","resolution":{"observed_at":"2026-08-16T05:13:10.968897Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.01892","last_updated":"2020-06-02T19:17:58Z","snapshot_observed_at":"2026-08-01T09:02:55.956548Z","submitted_at":"2020-06-02T19:17:58Z","title":"Finite Difference Neural Networks: Fast Prediction of Partial Differential Equations","version":1},"cited_work":{"arxiv_id":"2006.01892","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.01892","snapshot_observed_at":"2026-08-16T05:13:12.092807Z","title":"Finite Difference Neural Networks: Fast Prediction of Partial Differential Equations","venue":"stat.ML","work_id":"2773596e-630a-42ac-9a86-119ad672e2de","year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.972405Z"},"links":{"cited_paper":"/paper/2006.01892","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:85ac6dc0728d54280cd2868177090cbdbfb931b7a83d08222e9b283d69b7a5bc","observation_id":"e1b6bf8d-6a7f-4f20-9fc3-87b9c557dd94","resolution":{"observed_at":"2026-08-16T05:13:12.097700Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:10.976125Z","title":"Sukumar \\ and\\ author A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.976125Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:eac430ad813a732957398f793da2691f2b273cb10ef33148a2e2798038f40d46","observation_id":"16c7e706-2cc1-43cf-9364-e06a2134e70c","resolution":{"observed_at":"2026-08-16T05:13:10.976125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.979461Z","title":"Wang , author Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.979461Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f0dd5c7eb1fe20db2d897399d74f9b133de06a9f690758b8b1c45045545a81d8","observation_id":"df5f7504-bb31-47b8-98f6-083de40835d4","resolution":{"observed_at":"2026-08-16T05:13:10.979461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.983488Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.983488Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:fd70da6736c1e9f9c1ece5e2064c866c6655b69a637a9c3f4d35806836d0de0e","observation_id":"d38564ea-fcce-4d65-8e5c-4b02efee7752","resolution":{"observed_at":"2026-08-16T05:13:10.983488Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.986908Z","title":"Goswami , author C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.986908Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:56c368ba3d9fff019cc7558224906e1d828b1234bbb37131f466ce8848034c44","observation_id":"84d51b37-e569-4aaf-993a-91e6fee7d7ed","resolution":{"observed_at":"2026-08-16T05:13:10.986908Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.990134Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.990134Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:828695e42174145e99ca5b104448211261369a5f78c8e3770aa419cc7f4fe251","observation_id":"8e606146-2e2a-45f7-a566-2c87b742526c","resolution":{"observed_at":"2026-08-16T05:13:10.990134Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:10.993751Z","title":"Penwarden , author S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.993751Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:c6d0cd02aa8db5f5f120e5f1d7baad183d67278dd5ab88aa1bacc196b2a24fe2","observation_id":"64a73939-b4e8-456d-a1bc-44c4c6b368cb","resolution":{"observed_at":"2026-08-16T05:13:10.993751Z","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":"2026-08-16T05:13:12.607259Z","title":"Krishnapriyan , author A","venue":null,"work_id":"593d05be-8b85-4188-a2f4-345954d03c51","year":2021},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:10.996943Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:5dc0dd8388ad3d987d2240f4ea189c3e46f19438b799b6add89160bb5227ddc9","observation_id":"c6f63bf7-8ee8-477c-9318-20954191b1aa","resolution":{"observed_at":"2026-08-16T05:13:12.611152Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.08468","last_updated":"2023-08-16T16:19:25Z","snapshot_observed_at":"2026-08-19T22:01:40.703579Z","submitted_at":"2023-08-16T16:19:25Z","title":"An Expert's Guide to Training Physics-informed Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.08468","snapshot_observed_at":"2026-08-16T05:13:11.000356Z","title":"Wang , author S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.000356Z"},"links":{"cited_paper":"/paper/2308.08468","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:89cc8a0f296859b6255a4dafe1e788d707fd9f3ca663f851ee26432e57aa69df","observation_id":"73b2a603-4fe1-45cf-a796-e223e660a562","resolution":{"observed_at":"2026-08-16T05:13:11.000356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.004134Z","title":"Wang , author Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.004134Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:d8497708ed708f8e3a16ed24195d7e890ed241e9b50e8d6e9b5372f152408e95","observation_id":"0f7b6058-4c15-4182-8e95-a094e2103520","resolution":{"observed_at":"2026-08-16T05:13:11.004134Z","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":"2026-08-16T05:13:12.596559Z","title":"Rahaman , author A","venue":null,"work_id":"92c94315-48d7-4272-b506-0fe1ee9b9823","year":2019},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.008100Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:538846f9722c7085bae0dd6de9b970e2f158d5eb85c8918b544255fe8a21b35e","observation_id":"548572bd-a608-4306-b9a3-74af2462e275","resolution":{"observed_at":"2026-08-16T05:13:12.600304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.011355Z","title":"Wang , author X","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.011355Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f86fd5baf583def6489366afd1cc4092bf1df61973e0da6532725f62a852e96b","observation_id":"d98b9121-c64a-48c2-924f-2ce1d8e93c7a","resolution":{"observed_at":"2026-08-16T05:13:11.011355Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1705.07115","last_updated":"2018-04-24T06:42:35Z","snapshot_observed_at":"2026-08-17T06:56:20.691119Z","submitted_at":"2017-05-19T17:56:57Z","title":"Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1705.07115","snapshot_observed_at":"2026-08-16T05:13:11.014454Z","title":"Kendall , author Y","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.014454Z"},"links":{"cited_paper":"/paper/1705.07115","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:c5742c11f0afe06aeee2a53958d7ac3f2a8371c049b3a8db20dcdeab5e123a0c","observation_id":"156ae78a-cb1a-4bbe-8e22-d01e84f1c33f","resolution":{"observed_at":"2026-08-16T05:13:11.014454Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.018120Z","title":"Xiang , author W","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.018120Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f1bb119fe022236df9c9351656d008249935c17ebeaa57bdadea72a5a6815d0f","observation_id":"2dc345ee-9145-46e6-b968-2e8b9f1c084d","resolution":{"observed_at":"2026-08-16T05:13:11.018120Z","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":"2026-08-16T05:13:12.586134Z","title":"Tancik , author P","venue":null,"work_id":"b87471c8-ae0c-47c8-ac03-58a614905ed7","year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.023006Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:acef5c5777c29c279f8e596245dfef53875f3e88ae13d5d821b26f9ed6c1fe6d","observation_id":"fb1e0092-b23c-4676-8855-e80dec2a9738","resolution":{"observed_at":"2026-08-16T05:13:12.589633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.026322Z","title":"Wang , author H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.026322Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:e094498a19ea64c8ae14da9954569dc448527e949ebb82e29e9405a4850e5561","observation_id":"1361fffb-f825-4ca5-90cd-b55f11867360","resolution":{"observed_at":"2026-08-16T05:13:11.026322Z","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":"2026-08-16T05:13:12.575632Z","title":"Jacot , author F","venue":null,"work_id":"d6294038-1a86-4917-9b65-4dea2d1d36be","year":2018},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.029810Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:c3f272f220d95bb8231382c5703c2bc0f6fd916432ee0d44723b4c1a9a810a90","observation_id":"43d12340-35c8-4e7b-80ed-177c7e7c658d","resolution":{"observed_at":"2026-08-16T05:13:12.579078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.033906Z","title":"Mojgani , author M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.033906Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:78a74b0f15a146ecdd25c33d36356296846eb95c09e2f7db89a8193be1067e83","observation_id":"d34a5a84-6f75-4e02-9a77-b14eb3c566e6","resolution":{"observed_at":"2026-08-16T05:13:11.033906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.037436Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.037436Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:56dfcf12d8634d9146c0699d327fa21b7b9b6f3294ab98f32985d94f597e5912","observation_id":"7038e266-26db-4952-812a-d11ba0913f61","resolution":{"observed_at":"2026-08-16T05:13:11.037436Z","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":"2026-08-16T05:13:12.564564Z","title":"Wienands \\ and\\ author W","venue":null,"work_id":"dc146d9f-7545-4a80-8a03-56b62df14b23","year":2005},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.040948Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:f6a50a96ebbcb858926a6f77ca67605e3b353348cd2ac5302dfe1c9796e9725b","observation_id":"42af291b-a908-427a-8031-fe724d87e6fe","resolution":{"observed_at":"2026-08-16T05:13:12.568048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.11098","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.541929Z","title":"Margenberg , author D","venue":null,"work_id":"45327917-ab71-4550-89d0-555ddefb3a0f","year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.044274Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:714efea9c4405c0cc134103c71abbe9d72b213857b22d04198a29a9263add6c0","observation_id":"0ea70a9f-a4fc-494d-a200-dfc473f6dc17","resolution":{"observed_at":"2026-08-16T05:13:11.547473Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.047547Z","title":"Margenberg , author R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.047547Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:08cb6cf74dca6c9b5dbf720d2496378039467ab5c04edaeb057af754ef5160f0","observation_id":"7bce5bc7-7487-4b75-ac53-2b5c2438ae82","resolution":{"observed_at":"2026-08-16T05:13:11.047547Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.050954Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.050954Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:dd991e30a0f6cfff540cf8adf2d6f901dabe6b111ded7a41b5c34a28d7f05743","observation_id":"a1c8528b-f312-41bc-be5e-972f70497b08","resolution":{"observed_at":"2026-08-16T05:13:11.050954Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.054423Z","title":"Wu , author M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.054423Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:a8e6c33331279112b334e10984a780d60a814d8d3e701413ba3a24d023c2bc56","observation_id":"5dcc7e97-c148-4e98-b061-dbaa6fc78cc8","resolution":{"observed_at":"2026-08-16T05:13:11.054423Z","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":"2026-08-16T05:13:12.554036Z","title":"Riccietti , author V","venue":null,"work_id":"1dcaf9e1-0fca-44b3-aa2d-3e489c1faed6","year":2022},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.058183Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:b8efe8cf973d18217aca9b6c1b495071db0c06e4c309a5740f9d1f183182bb65","observation_id":"13e74ab7-c998-4635-96fa-9850d09e09de","resolution":{"observed_at":"2026-08-16T05:13:12.557797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.061627Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.061627Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:881b159bbf647e07a5b468565e847885b913a11d691fd01aa48625b969f1f4f4","observation_id":"348e2c84-0b44-4445-9a00-334a9c0e017d","resolution":{"observed_at":"2026-08-16T05:13:11.061627Z","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":"2026-08-16T05:13:12.543008Z","title":"Torrey \\ and\\ author J","venue":null,"work_id":"287e22d3-d1e1-4455-9826-9aad34b7d859","year":2010},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.065061Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:6ae055d6a275b7ab15482dd714fac0a5bd358152d66ec2506ceeca62f0f7616a","observation_id":"52bf0b17-89c7-401a-b24e-c850691a0c0b","resolution":{"observed_at":"2026-08-16T05:13:12.546772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.068387Z","title":"Cheng Wong , author C","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.068387Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:39d5553e1f8af230590ddf1f3139e5575fc852e4206834dc520b0d1e47e9b220","observation_id":"eee5e245-fd41-4500-8d9b-4eba6d320986","resolution":{"observed_at":"2026-08-16T05:13:11.068387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.05941","last_updated":"2017-10-27T17:45:21Z","snapshot_observed_at":"2026-08-08T18:23:31.977872Z","submitted_at":"2017-10-16T18:05:45Z","title":"Searching for Activation Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.05941","snapshot_observed_at":"2026-08-16T05:13:11.071529Z","title":"Ramachandran , author B","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.071529Z"},"links":{"cited_paper":"/paper/1710.05941","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:a9b53b5442219b2c57e0d6374b34067d2984a2ca17d5147e96f33264fcf246c2","observation_id":"dddfbe30-b721-411b-915f-b9387ae51348","resolution":{"observed_at":"2026-08-16T05:13:11.071529Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.075078Z","title":"He , author X","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.075078Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:5eb02a64c407a861c1369563f6bb6250caf483c31cc4287adcd5a75cdfd46597","observation_id":"52f8ffff-ac7a-4912-9548-583701e0464a","resolution":{"observed_at":"2026-08-16T05:13:11.075078Z","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":"2026-08-16T05:13:12.533091Z","title":"Sitzmann , author J","venue":null,"work_id":"a0e0cdac-824b-4513-b9c3-89d3e85d25b9","year":2020},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.078793Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:196727e012eddfef1445b019c94834a00d3a234222a3d567c756fd5ee63a7ac1","observation_id":"d236b841-027e-430c-847d-f518ab404a21","resolution":{"observed_at":"2026-08-16T05:13:12.536478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.521102Z","title":"Paszke , author S","venue":null,"work_id":"ddf9f17b-d3ab-4b19-a4a4-79547401b92a","year":2017},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.082004Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:e9e859309727fe7d395eae5cf80c2f3dac7639b84ce32ada8c0ceda01e706527","observation_id":"a8a5823b-3605-48a2-b514-24725f83aca4","resolution":{"observed_at":"2026-08-16T05:13:12.525722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-08-17T19:26:44.032537Z","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":"2026-08-16T05:13:11.085434Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.085434Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:0fca48a4956b8fa2f8a09a69eccdbe26c8c9b944c836a98c0ade49d21059919e","observation_id":"fdcb64fe-ebb6-4d84-9af8-7023cf14d4c3","resolution":{"observed_at":"2026-08-16T05:13:11.085434Z","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":"2026-08-16T05:13:12.509320Z","title":"\\ Chou \\ and\\ author C.-A","venue":null,"work_id":"a5b310c8-5879-4fa7-9870-d816db9be2f5","year":2023},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.088990Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:7dad0f50c3eb9438af6b6778937372a6c4923e1767eff4b1cdc25bc0a274f984","observation_id":"1afccdc4-7836-40cf-8f3c-55bfff3cbc35","resolution":{"observed_at":"2026-08-16T05:13:12.513107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/10407788208913458","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:13:11.146611Z","title":"Smith \\ and\\ author A","venue":null,"work_id":"468e22e5-ca0d-492a-850c-cf2f3a9ffb43","year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.092236Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:4599e211eca5fff07134db373b186d90f3af252f38ec0c81ddaaf4b5bf37d6bc","observation_id":"574ca6a2-43bd-4f84-8b05-84b5ceeb759c","resolution":{"observed_at":"2026-08-16T05:13:11.151062Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.095526Z","title":"Ghia , author K","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.095526Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:64f79802f5d2345bd06276d8a44dd86637eec45c7348a75dae632564baad30cc","observation_id":"72852b84-01a0-4a2b-9237-52960ef84efa","resolution":{"observed_at":"2026-08-16T05:13:11.095526Z","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":"2026-08-16T05:13:12.498556Z","title":"Li \\ and\\ author X","venue":null,"work_id":"73329d38-e634-422b-957f-b651344022a3","year":2022},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.098909Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:7563ea761a273377937395a2333fdebeba1458fcfdb9a46aa138f6e9ccba0ce5","observation_id":"041916eb-a73b-48b2-b306-8518d6c48bf1","resolution":{"observed_at":"2026-08-16T05:13:12.502108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.487799Z","title":"Karniadakis , author Z","venue":null,"work_id":"cd03a772-aa31-4e39-96a3-3b3ac398f329","year":2023},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.102015Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:22fadaf2e8113d2dd671a1bbc4c30dfc44f4a5535c728301cc908f2041976b68","observation_id":"bb67600d-a04f-4124-b5ac-7efd889335ac","resolution":{"observed_at":"2026-08-16T05:13:12.491335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.476247Z","title":"Jiang , author C","venue":null,"work_id":"b476eca7-e77d-4df6-b1bb-b5180c4e4049","year":2023},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.105403Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:8c55405d11a2a8c61e47a8e9a07625b9163f21f55f1fb178330a224899bd42b9","observation_id":"43917a75-de4e-4c83-a13e-e16a13f1e33d","resolution":{"observed_at":"2026-08-16T05:13:12.479900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:12.464382Z","title":"Chen , author R","venue":null,"work_id":"04d8393b-0a96-4366-abca-b2052a0f840c","year":2021},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.108440Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:96fe571ad7ab6734538524f2c09cbc274a2d0324ca5551c4010f10e2f0042012","observation_id":"a2f20487-5103-4141-b976-4a6e5c321fc5","resolution":{"observed_at":"2026-08-16T05:13:12.469082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T05:13:11.111534Z","title":"Jin , author S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-16T05:13:11.111534Z"},"links":{"citing_paper":"/paper/2504.21328"},"observation_digest":"sha256:36a31daad1120c1987443b1f2c35693a86cfdee43f2fce6fb8b1d710034754c6","observation_id":"c24361b0-50cb-4c77-bfe3-e6273c9d4eef","resolution":{"observed_at":"2026-08-16T05:13:11.111534Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2504.21328","last_updated":"2025-04-30T05:30:27Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-17T22:42:21.615326Z","submitted_at":"2025-04-30T05:30:27Z","title":"Multi-level datasets training method in Physics-Informed Neural Networks"},"reference_resolution":{"displayed":61,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":42,"verified_exact":2,"verified_fuzzy":16},"total_outbound_references":61},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 0 inbound Pith citation observations for arXiv:2504.21328."}