{"as_of":"2026-08-13T12:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c1cf6da83e8c7de590abce4613545a4be05d724bb163b1c588cf09e12c3b8de8","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:40:59.950549Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-03T02:29:11.422793Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T02:37:34.134519Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"cited_work":{"arxiv_id":"2501.07700","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.07700","snapshot_observed_at":"2026-07-03T02:37:34.134519Z","title":"Celaya, D","venue":null,"work_id":"a5ee772c-64db-405f-8604-b686fda9efe8","year":2025},"citing_paper":{"arxiv_id":"2607.01749","last_updated":"2026-07-02T06:06:56Z","snapshot_observed_at":"2026-08-03T22:24:42.019236Z","submitted_at":"2026-07-02T06:06:56Z","title":"Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-07-03T02:29:11.422793Z"},"links":{"cited_paper":"/paper/2501.07700","citing_paper":"/paper/2607.01749"},"observation_digest":"sha256:88b782f2a041af1552b386d3f744e52eee558e7219f81e2bd70d164c40c96045","observation_id":"e87b82a6-7e06-4775-98eb-86b704ee5515","resolution":{"observed_at":"2026-07-03T02:37:34.136210Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.07700/citation-record","integrity":"/paper/2501.07700/integrity","json":"/paper/2501.07700/citation-record.json","paper":"/paper/2501.07700"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:40:59.778653Z","title":"Physics-informed machine learning,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.778653Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:de144e5ebe5b211f9bc1dc5db21fcd3513bf4a5c3f802df07f9280930badb2c3","observation_id":"95398225-48e9-4556-945c-092221d89e0b","resolution":{"observed_at":"2026-08-10T20:40:59.778653Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.578528Z","title":"DeepXDE: A deep learning library for solving differential equations,","venue":null,"work_id":"411bacda-ec27-48c3-b3f4-68591ff925cf","year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.783762Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:fe87884e6780b3291aa5e9d73428dca085daf876afcf3b1f2d60c7fb24a5fec0","observation_id":"056aafde-db80-4f1f-b546-e101f9d70dd6","resolution":{"observed_at":"2026-08-10T20:41:00.583883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.562648Z","title":"Physics-informed neu- ral networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,","venue":null,"work_id":"92655c2c-d762-445e-910e-e6700b6a04b7","year":2019},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.788388Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:1518e0c30ea053bc937255a6da7b5b7ce8ccb96b83dd2b7bb1cd21397c56c8f1","observation_id":"fda9f14c-39ed-4579-b2db-7a084a853d54","resolution":{"observed_at":"2026-08-10T20:41:00.567743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:40:59.793102Z","title":"Physics- informed neural networks (PINNs) for fluid mechanics: A review,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.793102Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:d6a0a883f279467ad4fd82e8c2d07c5d7b61f59b879c7507b3259d75f17cb87a","observation_id":"4694a78c-324d-402c-84da-02cf571a0553","resolution":{"observed_at":"2026-08-10T20:40:59.793102Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.536807Z","title":"Multiphysics- informed neural networks for coupled soil hydrothermal modeling,","venue":null,"work_id":"dd1475d1-4b0c-4ec3-b09c-1bb3547375e8","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.797849Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:3cda40950412c92eefb0ab2942eec585595c513d26db4a978833ffe13438d4ff","observation_id":"4c4a86ed-dbc2-4525-9e52-9ac30d05cb67","resolution":{"observed_at":"2026-08-10T20:41:00.541627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.521465Z","title":"3D multi-physics uncertainty quantification using physics-based machine learning,","venue":null,"work_id":"6006cc8e-a47c-4662-bd4b-d9f88342abe2","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.802796Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:20d400ec764371bde0a10ab6437b923d0ac99d1a7481c627fc086eb85ace763d","observation_id":"af5b6f71-e9bb-4b31-ab13-bc60d5840166","resolution":{"observed_at":"2026-08-10T20:41:00.526456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.506464Z","title":"Systems biology informed deep learning for inferring parameters and hidden dynamics,","venue":null,"work_id":"8b1b7fd0-8fef-4e9b-bf5a-e4efad3e2f30","year":2020},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.807736Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:985b35a36143d7a048cf151dfe8a37f8af9cdddc9d5f7df7976c40a69cdb7588","observation_id":"e58d4cc0-7903-46da-8e0e-017a7e72bc80","resolution":{"observed_at":"2026-08-10T20:41:00.511202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.491633Z","title":"A comprehensive study of non-adaptive and residual-based adaptive sampling for physics- informed neural networks,","venue":null,"work_id":"ed2009e3-5b47-4c60-a4d3-b929e5cc6a80","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.812552Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:77a855cd1b799c4ffc5cb977d2a672b191871d86648e5d574381ffad0d9e47b8","observation_id":"a1b70bb9-7bea-42db-adcd-9a86a5082dcd","resolution":{"observed_at":"2026-08-10T20:41:00.496633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.476272Z","title":"Meta-learning PINN loss functions,","venue":null,"work_id":"d217ed85-3454-4e79-95bf-72576afc6fab","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.817413Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:e24636d9960aba483ea64d3dffe72f743250e11eb53e183a2d02a01fad3073d1","observation_id":"61cf1afd-688f-4989-80ab-1569a9750174","resolution":{"observed_at":"2026-08-10T20:41:00.481040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.460514Z","title":"Gradient-enhanced physics-informed neural networks for forward and inverse PDE prob- lems,","venue":null,"work_id":"1a044622-04e1-49d3-bd9f-64f503c83609","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.821851Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:ba17103db0cd307d1883008b12565a2b6f3a432e154bb526453c3e27d1b51455","observation_id":"d44f4436-3b34-41c9-82c2-609e3a395f76","resolution":{"observed_at":"2026-08-10T20:41:00.465713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.445490Z","title":"NAS-PINN: neural architecture search- guided physics-informed neural network for solving PDEs,","venue":null,"work_id":"10222fad-2ccc-4824-ad8b-3807b1aee548","year":2024},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.826168Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:9a34fc535a90662fe4d907af5ebc7db39812bc199653bbf2e0a71d93657b5792","observation_id":"af397fab-d7ec-4752-92d3-935d9b2cec82","resolution":{"observed_at":"2026-08-10T20:41:00.450367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.430607Z","title":"Physics-informed neural networks with hard constraints for inverse de- sign,","venue":null,"work_id":"a3763938-3966-4aa5-80bd-87118659ac96","year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.830755Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:d16ca34ba56d8b9f7dfedb023550a0dfc704807e9b4431fa45e7302f80c2e126","observation_id":"f265b0ba-a37c-4321-8589-bad87ef001a0","resolution":{"observed_at":"2026-08-10T20:41:00.435679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.415460Z","title":"fPINNs: Fractional physics- informed neural networks,","venue":null,"work_id":"7879e570-c539-4f34-99e2-48e15ccf0fea","year":2019},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.835170Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:9c186071336e667f7f3b66dfe6909ca12a585f4d8c8206eab18c216a38ccc19b","observation_id":"78e96417-b7c3-43ca-8bbb-8aa3c28b1afd","resolution":{"observed_at":"2026-08-10T20:41:00.420052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.400875Z","title":"Adaptive deep neural networks methods for high-dimensional partial differential equations,","venue":null,"work_id":"46f1ea71-a285-4bc8-b958-944a62dcbfac","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.839397Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:a9c08965245173c48b35e60fa9c42b4cf36e3082843fc128e8087cb1a98ef53f","observation_id":"cf40274f-942f-4be8-96f0-21e3e1c5a739","resolution":{"observed_at":"2026-08-10T20:41:00.405799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.386934Z","title":"Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks,","venue":null,"work_id":"763d8201-d62d-4e8a-b9ee-ccabb6d22e18","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.843897Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:1c1bc6db6f6faa033a6bcfcad29f4b843caafbd6a6722ca7366538f376d3e6aa","observation_id":"ea69b297-8f4e-46bd-a296-b487a026d0f4","resolution":{"observed_at":"2026-08-10T20:41:00.391633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.371335Z","title":"Efficient train- ing of physics-informed neural networks via importance sampling,","venue":null,"work_id":"7f9d17d3-1f5e-4744-9c9f-fc7be260c792","year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.848290Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:92edd014421dc0bb3d1f6a29895b6ff92745ac8e462594c402b7fbf7ab04df97","observation_id":"9704b257-72ba-432b-9afb-b7bca42fc918","resolution":{"observed_at":"2026-08-10T20:41:00.376024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.356912Z","title":"Investigating molecular transport in the human brain from MRI with physics-informed neural networks,","venue":null,"work_id":"878acd9e-9ecd-4ae8-827c-4ecd8526bb74","year":2022},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.852552Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:6c90fd5a6a77978755531c21acfc5de9daffed79c6825d58052f291bab5b6431","observation_id":"430c497a-0439-4cde-800a-40581b555d79","resolution":{"observed_at":"2026-08-10T20:41:00.361557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.340572Z","title":"Active learning based sampling for high- dimensional nonlinear partial differential equations,","venue":null,"work_id":"6982bef2-54f8-4abc-85bd-da9d3af5ce13","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.857185Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:65edbf8619f29532beaef9c4b03ed3ba227a4ea1b15221bc45a512f592c7d43f","observation_id":"ac42152e-8565-48f5-8929-129c4237ad31","resolution":{"observed_at":"2026-08-10T20:41:00.346228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.324672Z","title":"Miti- gating propagation failures in physics-informed neural networks us- ing retain-resample-release (R3) sampling,","venue":null,"work_id":"b5e8fa17-2d47-4686-abb9-e2e1b3ced4ba","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.861905Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:0c0018e9d35b389e2a3970951c1bd52d01e63e3ae8e9242b3c3cfd36790459d6","observation_id":"732e8dac-8c05-44b7-a053-da3894e66a13","resolution":{"observed_at":"2026-08-10T20:41:00.330007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.308777Z","title":"PIN- NACLE: PINN adaptive collocation and experimental points selection,","venue":null,"work_id":"3ccbaa64-b2d3-47e8-a584-24e84c59fb10","year":2024},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.866507Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:f1d72844c57aaefea00a1246af375b48be26785ddbe47e757a6628244b26f187","observation_id":"2c399edb-98e0-4672-bb4f-214d9f4fd6e6","resolution":{"observed_at":"2026-08-10T20:41:00.314203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.292658Z","title":"Nonlinear model reduc- tion via discrete empirical interpolation,","venue":null,"work_id":"c3b6e8d3-584c-476f-9d97-fca7dc2a2d51","year":2010},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.870919Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:5e0673c54d9747b9150103b86379c3dec8898910ad8144465f4751bddef53c83","observation_id":"47cec172-c71d-4ef1-b51b-d1106007bd10","resolution":{"observed_at":"2026-08-10T20:41:00.298340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.275928Z","title":"A new selection operator for the discrete em- pirical interpolation method—improved a priori error bound and exten- sions,","venue":null,"work_id":"4c57bf85-fa5f-4d9d-b295-2ac54f66d53a","year":2016},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.875494Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:b39a516eddfa7982e993dea341b15bd3c984804d1882232308195fe844e01eaf","observation_id":"01114c13-a8d6-4753-b11b-e75144bb1ca5","resolution":{"observed_at":"2026-08-10T20:41:00.281396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.08537","last_updated":"2024-05-14T12:21:08Z","snapshot_observed_at":"2026-08-13T00:08:04.538575Z","submitted_at":"2024-05-14T12:21:08Z","title":"GS-PINN: Greedy Sampling for Parameter Estimation in Partial Differential Equations","version":1},"cited_work":{"arxiv_id":"2405.08537","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.08537","snapshot_observed_at":"2026-08-10T20:40:59.986994Z","title":"GS-PINN: Greedy Sampling for Parameter Estimation in Partial Differential Equations","venue":"math.DS","work_id":"1fffe67f-59ae-4072-b951-e1b4a89f64e9","year":2024},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.879664Z"},"links":{"cited_paper":"/paper/2405.08537","citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:f59d140cf553d2611e6365d7543a72c147d7d53026240ed9f8cfaced6a924ec9","observation_id":"4677de0c-5630-481e-92a2-d727cc4073c4","resolution":{"observed_at":"2026-08-10T20:40:59.993994Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.258450Z","title":"Projection methods for reduced order mod- els of compressible flows,","venue":null,"work_id":"75975ca4-e6dd-4630-80c8-d99e5842dbd9","year":2003},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.884250Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:6e0f3c86c070763163d08cafeb7cc6f349a7a03bd4822683de422bd976274387","observation_id":"22a660f6-8c0a-4e80-a53a-a9e9d34eedad","resolution":{"observed_at":"2026-08-10T20:41:00.264542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.241179Z","title":"Stabilization of projection-based reduced- order models,","venue":null,"work_id":"7bae9218-62b6-424d-b850-3f715a8562cf","year":2012},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.888530Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:4a6ddec0ba59b1e0e0c299e407f2f9247845fe1bdb69281af85a8c3ca87b4880","observation_id":"bedc2999-790c-415a-a399-25628c2908bf","resolution":{"observed_at":"2026-08-10T20:41:00.246612Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.226032Z","title":"On projection- based algorithms for model-order reduction of interconnects,","venue":null,"work_id":"9012f9d9-b33f-442d-9699-823964af9643","year":2002},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.892764Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:a420682d3e90b914783f90259710534af1340ce356228242bff1d23c1708857e","observation_id":"b2019bff-ea88-49ca-accc-766d6ea6f197","resolution":{"observed_at":"2026-08-10T20:41:00.230776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.209550Z","title":"Proper orthogonal decomposition extensions for parametric applications in compressible aerodynamics,","venue":null,"work_id":"76f2e36e-20e9-40a3-9ffa-865c1c7c286f","year":2003},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.896942Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:a2b603475c76fc6b0227c7ccb3fec45572d7c28a76de0801391aa3de23039399","observation_id":"89bdddcc-ce85-4303-9844-02e634a5085a","resolution":{"observed_at":"2026-08-10T20:41:00.215441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.192697Z","title":"The proper orthogonal de- composition in the analysis of turbulent flows,","venue":null,"work_id":"0fa925a6-9c9e-440c-ae91-8d417de35f78","year":1993},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.901104Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:13b0af330b73cae08d8837cc8ce2d7d42b9123ea60bd3497f44a33768e7fac02","observation_id":"7e6b68f3-a99b-41c8-9bd2-fba456e03beb","resolution":{"observed_at":"2026-08-10T20:41:00.197862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.176214Z","title":"A reduced-order approach for optimal control of flu- ids using proper orthogonal decomposition,","venue":null,"work_id":"ef85ba22-13ba-44fe-b547-da2a9763c32a","year":2000},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.905246Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:e4e7316aae6e94357c787a679f06125b24b2c591c1aaf1f3decae45cabceb87b","observation_id":"1d72968e-0cba-4b13-8333-a4d01bfbb3f5","resolution":{"observed_at":"2026-08-10T20:41:00.181451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.160199Z","title":"Proper orthogonal decomposition for linear-quadratic optimal control,","venue":null,"work_id":"8db23384-c60d-443a-a38a-7af052bcc573","year":2017},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.909887Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:e631d1ae91c2101560a9db01c237a6c235d5cd959d75d94ce6bbd2d8ab544ad7","observation_id":"69537d96-e037-40e3-81e4-40f2dea024c0","resolution":{"observed_at":"2026-08-10T20:41:00.165294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.143668Z","title":"Nonlinear model order reduction via lifting transformations and proper orthogonal decomposition,","venue":null,"work_id":"07718c01-b549-4d3e-872c-d4b736971a19","year":2019},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.914280Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:427ed77cbe9f7e36bc41c1904a4295d826ca039e1a7999e2b038ce133699b7d3","observation_id":"c32cc432-fc58-4730-828c-64bc5f65ca32","resolution":{"observed_at":"2026-08-10T20:41:00.148589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.127850Z","title":"Discrete empirical interpola- tion for nonlinear model reduction,","venue":null,"work_id":"1d89f143-2e19-4ea2-9326-01584903b75f","year":2009},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.918760Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:28f1b33319a4aa270d6bc1e79aaa2b4271ac088885e7ec49d7924762ec36cf05","observation_id":"6cc2b6da-9f3f-4711-ae42-6003a8234561","resolution":{"observed_at":"2026-08-10T20:41:00.132939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:40:59.923192Z","title":"Finding structure with randomness: Probabilistic algorithms for constructing approximate ma- trix decompositions,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.923192Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:d659cde2e71c034142a21ff8d3e00a2779bdd52cb9d8dccf747ac7fd84c950c1","observation_id":"d0bf262c-3c4d-4355-818a-c3c7349530f7","resolution":{"observed_at":"2026-08-10T20:40:59.923192Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.101454Z","title":"Challenges in training pinns: a loss landscape perspective,","venue":null,"work_id":"aa663e54-7eb7-4445-a209-8b626b86cd16","year":2024},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.927583Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:bdd083cdae7ddb855a498a4c26a6ba44d9edc2d92d9b23a8729dc8453b3005a5","observation_id":"6d7e7bbc-c2e7-424e-a4fd-2ba72185b055","resolution":{"observed_at":"2026-08-10T20:41:00.106263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.083714Z","title":"Characterizing possible failure modes in physics-informed neural net- works,","venue":null,"work_id":"5cd47b6f-dc2d-4bfd-a685-f1a59d25b4c1","year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.932527Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:88d39b71f3cce20acbdf24ccdc9c9fc85873fee923b93e5f509696e2eddb2e7d","observation_id":"0bd281bb-dbe4-4e79-aff2-b915799b4ead","resolution":{"observed_at":"2026-08-10T20:41:00.089549Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.067604Z","title":"Kolmogorov n– width and lagrangian physics-informed neural networks: A causality- conforming manifold for convection-dominated pdes,","venue":null,"work_id":"bc3caf7c-a519-4fa4-a9b0-2d091227f9ca","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.936973Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:db6eca2c6439a539253130612e8256b2e7c5648d3e649c498294aa445336ac72","observation_id":"1371866a-1adb-464d-b282-aa4ce62ffc38","resolution":{"observed_at":"2026-08-10T20:41:00.072860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.051342Z","title":"A unified scalable framework for causal sweeping strategies for physics-informed neural networks (pinns) and their temporal decompo- sitions,","venue":null,"work_id":"9209f675-9515-43db-8839-aaced18f209b","year":2023},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.941421Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:c2fbd13c57a6b2789b7cd906471aed9d7477acdefaeea96a7574b271fcaeea04","observation_id":"d8fff5fa-8dbf-42a8-a313-1b168e923aeb","resolution":{"observed_at":"2026-08-10T20:41:00.056788Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.032874Z","title":"Extended physics-informed neu- ral networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equa- tions,","venue":null,"work_id":"5691653e-a08b-4894-8f18-591b1efc1e4f","year":2020},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.946236Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:c877437e1e4f38559bd0c5c3b0a269c4f4d564d3b670947f1844a9a517559fe4","observation_id":"7270da50-18b6-4053-9ddb-aed93a827074","resolution":{"observed_at":"2026-08-10T20:41:00.039451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:41:00.013665Z","title":"Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks,","venue":null,"work_id":"a978807d-2dde-40f6-9208-7939e3c89c4f","year":2021},"citing_paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method","version":4},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:59.950549Z"},"links":{"citing_paper":"/paper/2501.07700"},"observation_digest":"sha256:46ffa1e0f8a7ab7d96995bb19a607ea859e5880c0737876605a18e50f5adde33","observation_id":"55b7be42-7b78-41a7-ab4e-72a9212ea0ea","resolution":{"observed_at":"2026-08-10T20:41:00.020812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.07700","last_updated":"2025-08-07T20:32:05Z","latest_version":4,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-13T07:15:26.981124Z","submitted_at":"2025-01-13T21:24:15Z","title":"Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":35},"total_outbound_references":39},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2501.07700."}