{"as_of":"2026-08-21T05:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dc8e7f7f815c807c79931ca16210cdfb4b2eb8090f8b0cea9c9d30e1584df83e","coverage":[{"denominator":66,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":66,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T01:42:23.454308Z","state":"measured"},{"denominator":66,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":66,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2606.17513/citation-record","integrity":"/paper/2606.17513/integrity","json":"/paper/2606.17513/citation-record.json","paper":"/paper/2606.17513"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T01:42:23.454308Z","title":"Fourcastnet: A global data- driven high-resolution weather model using adaptive fourier neural operators, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e6a7bb38b7de89bede5d90f81217092b71fd70e1c793da12dbad89232bdfdd26","observation_id":"69518dc7-eddc-401b-a576-6dda1e35a118","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Spherical fourier neural operators: learning stable dynam- ics on the sphere","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:4eb17f9326ade1b2a49c9e19c5183bd29604195210f9d593f4be147b67e69ded","observation_id":"5c9febae-ed77-4fa9-9001-c4f98bf3a752","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Fourier neural operator for parametric partial differen- tial equations, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:121690585121dbbf6fe8b709a1dc745bc1bb2afb772ab4765a1091fc7a52fc3e","observation_id":"8fb5a243-d739-4f79-9d5c-1a43a4aefc70","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Yeh, Jean Kossaifi, Kamyar Azizzade- nesheli, and Anima Anandkumar","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:9579957d7e21ac04c23fc405b6a600558ba1531a04a34787a2a9f47bca8def57","observation_id":"fbe30cde-0e84-4712-bf8d-102815c353a2","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Fourier neural operator for plasma modelling, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:9e02e0356fe8be6c16cd66e2410b401a24c7031f9af3fd2ae80eba88966e70f5","observation_id":"8cc1a9ff-76f6-4c08-b34b-e55121726db3","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Carey, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:1e9f92892e60299f86d04f0bde29f74946b3bcd44bbe0683fbcb6486e960c9e9","observation_id":"d03e0528-9ebb-42e0-bfc5-782ebc37e96e","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Khorrami, Pawan Goyal, Jaber R","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:57ac415cfb550691e7767d3a68f6995fa8b0b460ac21eb05ff277b8f64a08338","observation_id":"56e94fac-3390-41f5-826f-98564468d2a6","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"A neural operator based hybrid microscale model for multiscale simulation of rate-dependent materials, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e90409c8a1f188ff79142b51917d4741344be29002a89904fcc8b6025c67a982","observation_id":"aa05da7a-63dd-4e4f-b854-3927ba2bb5f9","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Fourier neural operator with learned deformations for pdes on general geometries.J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:56b8bd90156708d15b22f3d2ae594caaa93e7bb9a2a24fa4fa83eed625dc10c9","observation_id":"4777f059-0338-49e2-a5c0-60df0d456c93","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Transolver: A fast transformer solver for pdes on general geometries, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e5b722974465442a00f881750380ac9b3c5363c02a88a0ce92afa0517dd9efe6","observation_id":"32bf955f-ab6a-4d02-9c89-1d6d8213bdc7","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Transolver++: An accurate neural solver for pdes on million-scale geometries, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:a8475662b328e963a4e36e4ab55f71ee074baabab3d41a5d548f36dbb1062c75","observation_id":"5f979f4f-1555-494c-9950-94cb191342c0","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Transolver-3: Scaling up transformer solvers to industrial-scale geometries, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:5d4f7f8fda85f82bc944d77ad111faa257255c00b003f9d1753c26c43a329a83","observation_id":"a3cb6946-2abc-4163-85af-106a78defe34","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Chandra Mouli, Danielle C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:fa409ba4db7441482960751ea3bb79f603c242c03615e0d684d5860ab2ccfcf0","observation_id":"fb3f249b-0422-475b-94da-3e52a86f0c50","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:9b65a7acfb523505871df356228fd8b65bcfc56bc0041741c9b48be7b9b8d3c0","observation_id":"840c9c18-be51-4503-9780-cde61a49325b","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Active learning for neural PDE solvers","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:5c54e2ff189825673d09dac801734f70d4cca59acba3e7c198afcc9ffd77a824","observation_id":"c77519cd-3f93-49eb-81a9-4ba0d6e7783a","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Simple and scalable predictive uncertainty estimation using deep ensembles","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:464596fe8a6d009a42de65b3a3535fb21a6ae5e917eb2bb31e96ae8067a3be93","observation_id":"290d3af1-5021-440f-a6d5-a2b48dec8375","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Dropout as a bayesian approximation: representing model uncertainty in deep learning","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:153f1f3e09d45e10cb97cd2366995cd1b072c21fd47dceaae94dad1c820265c8","observation_id":"5eafb7b4-d652-4399-bab9-b0d628103e83","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Light-weight diffusion multiplier and uncertainty quantification for fourier neural operators, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:b894a63a30dd0fb8477f6562495d374f3f27bc6527af2cbe96750d53f9c551a2","observation_id":"aea366e3-9123-447b-b15a-dd0b2a5fcea4","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Laplace redux - effortless bayesian deep learning","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:42731f71d932b0b637343e6dbcc612047f5645c5412dfa76acae18f620a75fef","observation_id":"78b24af4-a889-47e3-be6f-131bc0b5d3c9","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Linearization turns neural operators into function-valued gaussian processes","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:0ede8d93bedc9ba8d8985d80a843911f45d257c82d0463fbe6759d72cbf03e13","observation_id":"c5f54a56-c9cb-4a8b-9c5a-e820513e0847","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:a398eaaeba414a47971e3af633c946e3043c8659fabc8cbf33b020d0bc7f22ba","observation_id":"e7345766-9fa1-44be-b0cb-a442537d8865","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Operator learning with gaussian processes.Computer Methods in Applied Mechanics and Engineering, 434:117581, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e5787f2c8ae5b3cc47b4bc29137e72ec1a4b9ea250ebb2eaaa398695129820c7","observation_id":"2e230248-4693-426a-8eb2-2beb174f9e9b","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Kernel methods are competitive for operator learning.Journal of Computational Physics, 496, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:34aef6ab4b344301b1a0351229b820f5dd1b1fd3fc1a18c1a885bc3971d86604","observation_id":"a4ea13a4-b4c8-4c1c-be08-b8bc57a7a783","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.00809","last_updated":"2026-06-02T21:20:03Z","snapshot_observed_at":"2026-08-16T13:38:20.799434Z","submitted_at":"2024-06-30T19:28:12Z","title":"Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning","version":4},"cited_work":{"arxiv_id":"2407.00809","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.00809","snapshot_observed_at":"2026-07-03T20:08:55.688579Z","title":"Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning","venue":"cs.LG","work_id":"88053fa9-cb06-4583-89e2-afcf4f932cbb","year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"cited_paper":"/paper/2407.00809","citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:1fc38dcb3904eca4746904e8fb4a336829e4fefc243b86384239cea9ea8fedd9","observation_id":"73ad8316-fa8e-45c6-984e-decdb877818e","resolution":{"observed_at":"2026-07-03T20:08:55.690340Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-27T01:42:23.454308Z","title":"Error analysis of kernel/gp methods for nonlinear and parametric pdes.Journal of Computational Physics, 520:113488, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:8846de1a30e6e578534c98a3812a4186a18411cf474fb88a48c35f932d4626a0","observation_id":"0da2da73-c066-4c65-aee4-981ed78e92ea","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"On the brittleness of bayesian inference","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:48c28274bc778aed2e89c5fbb30d5051a5128c9de47a7ff800b40cc058343c07","observation_id":"ff5f01cf-bb1a-41d4-88ff-c4251eacfde5","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Kernel flows: From learning kernels from data into the abyss.Journal of Computational Physics, 389:22–47, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:eae99f3b4f7d2f8811e4d8bd4d7800340a472a5adffb363dbe257bddb5847e4d","observation_id":"aceca5e2-bf00-49c7-b9f5-1f167b8dfa53","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Geometry-informed neural operator for large-scale 3d PDEs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:b10427b29b7c9340eb04122cc7c286c6a3a644b3374d476f473de57bfee93b17","observation_id":"b14b4249-c57c-4490-a811-e8b1f4c9578d","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Kernel interpolation for scalable structured gaussian processes (kiss-gp)","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:f95add2ecf86da2406f82f7ce8b30830a68a59d9d8705c5cf9553261988618e6","observation_id":"6a501367-c7ed-4eb2-9b63-479c3ee01ee7","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:8c2874aa69efd1e6d49031dc5a3931e57282e5ba539c7c34bbeedea5971b6988","observation_id":"1d5be437-cba5-4d0c-ab2f-cdde48ab9f65","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Using the nyström method to speed up kernel machines","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:07dc54fa80345a61b80f7b3b436e369c37cffac83bc54c35a2adec694b1d0a10","observation_id":"3f54172f-9912-4b15-bee3-751149969989","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Variational learning of inducing variables in sparse gaussian processes","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:ba3cba7b89b01cfa80fb6affd2083ef2ef78932867f4ff93b970acd5f6365bc4","observation_id":"ffdb59b9-5d17-4fd2-b7a7-0087ffa683ce","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Scalable Variational Gaussian Process Classification","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:3481f2028c90b45d56875cd0cf804ffc20a0834822201aafc6a7eb8f7ab85b32","observation_id":"26b943e7-cd98-4478-9fa1-309cbaf9f738","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:25674b3fe359e6110c6f06676827183833345b8a8ad4bd324749665d1af80ee5","observation_id":"04dfdf2d-8ff8-4d36-b7e2-84233280d2d1","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Maddox, Timur Garipov, Pavel Izmailov, Dmitry Vetrov, and Andrew Gordon Wilson","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:9ec17627777da26bebd259c226e14b3c99077d651b8009e778d265365ba1db19","observation_id":"f2db5b75-45b0-42ff-87e7-3963b550c2bc","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Probabilistic predictions with fourier neural operators","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:ba3fa027e133a96b765d7a6988faeeb9108414822ef433d29aec19b2ded712ac","observation_id":"abf21765-20de-44ea-a81a-542419a09714","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Probabilistic neural operators for functional uncertainty quantification.Transactions on Machine Learning Research, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:32b8db2ffd9cb36931459b0ae208b4c9d85c02df68b5574e24bbb3e7d06cfb0e","observation_id":"65f46197-1c38-4880-8cdc-96b4b2089c31","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"A simple approach to improve single-model deep uncertainty via distance-awareness.Journal of Machine Learning Research, 24(42):1–63, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:634dc6efefd2174112d2e6e28e12761a3dc18ac8033bb37e3abaad726316d9fc","observation_id":"f829058d-0ac4-467e-9883-c382fcfbcd0d","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:bd9de79ba25f988e6b7d8ff437a05a7418851da83a0d7efc09661ffe23b35867","observation_id":"0a6f9b12-27d2-4d6a-9268-8ff58b528eb2","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"A scalable laplace approximation for neural networks","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:b8a366a774db5e0e1b81ad5e2f280c27868248269d334e1fe041dd9b79e8f099","observation_id":"4658404e-2043-4dd2-bd76-e3c166593757","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.01565","last_updated":"2022-08-02T16:10:27Z","snapshot_observed_at":"2026-08-16T16:41:40.066602Z","submitted_at":"2022-08-02T16:10:27Z","title":"Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs","version":1},"cited_work":{"arxiv_id":"2208.01565","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2208.01565","snapshot_observed_at":"2026-07-04T10:09:45.091849Z","title":"Approximate bayesian neural operators: Uncertainty quantification for parametric pdes.CoRR, abs/2208.01565, 2022","venue":null,"work_id":"7530c9e0-64f0-4481-8e7f-6457ba8acfa0","year":2022},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"cited_paper":"/paper/2208.01565","citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:8dac20e7e74733d352b42e5863ec5745dffc37f3f331ac224c353ad12e8a6e5a","observation_id":"dbf4c305-1caf-4d02-aa6f-cf9db44c75a7","resolution":{"observed_at":"2026-07-03T20:08:55.681504Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-27T01:42:23.454308Z","title":"Uncertainty quantification for fourier neural operators","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:a5382f296540961bcc7db6353541d95d5feec65193759ef77231ba2598e486dd","observation_id":"0b2cd81f-0c60-4e79-9688-c7356abd57b8","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Vecchia gaussian process ensembles on internal represen- tations of deep neural networks","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:03ec94d1217cd02089e32b46f5e859d51ec4cfdd61107478483891a75ba202bb","observation_id":"290dfa33-37e9-4f67-aad9-74062ae0daad","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Kennedy and Anthony O’Hagan","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e04b55c2d2e02f97e7742e60c2a112766442faf92794bcd5491e86980935d978","observation_id":"393a2b9b-5145-47ec-bd4d-eaca832b98eb","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Cavendish, John A","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:6f24315f873914216e39f5dafd291020fdb1e6118d514ffdb51f2e88e6008bd7","observation_id":"3f76bfb6-01e9-40ae-88aa-1f594d2eef41","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Computer model calibration or tuning in practice","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:e02a49173d159a81a4af626eb90a4f884bdde6ed70e302d23874b87d545d9b86","observation_id":"cede7d15-d804-4ff1-9ee2-89d70aec28b4","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"On the spectral bias of neural networks","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:dca44e62dc0b111d01e79ec3880d9d28df778e0df9bf087f71c976593fced65d","observation_id":"dd0a7ec0-0b9c-4c55-b451-0936be016777","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:1bdd729c42bf6fd838441ba8d5bdf8c6dc7d1e0734d0c8634a08eec9e57b884d","observation_id":"24a2ba93-d662-44bb-bb9c-e3201f508dac","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"parse_uncertain"},"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":"2026-06-27T01:42:23.454308Z","title":"Layer by layer: Uncovering hidden representations in language models","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:03e26bad2ca83a9f18b44f5cdfce605c67ef11e80d0be3c90918a51ac0641883","observation_id":"9d7dc7c8-510f-4349-9945-e7a43871663d","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Visualizing data using t-sne.Journal of Machine Learning Research, 9(86):2579–2605, 2008","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:ac5d3cd0ab7c43ff4fc52d829ac96e009a2e7c1ec38953fe081eb3b9370ae1f9","observation_id":"58e8a3c7-ba5d-44ca-966e-c9eb215afaf0","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Bayesian calibration of imperfect computer models using physics-informed priors.Journal of Machine Learning Research, 24(108):1–39, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:910a563d1f3ec6e64c57a31ec0d68a4d543ff14079a87cb7a5c6275827afe386","observation_id":"ea0517f3-7143-4a03-8cf1-e2622859e322","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:da4b357b5765ef150bea1bac42d7f3db86b65583d8d25c3d9b1829385e501599","observation_id":"6e7fc0f3-ef7b-41bb-9c0f-7919c12d8c32","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.00414","last_updated":"2019-07-19T14:59:45Z","snapshot_observed_at":"2026-08-18T09:29:11.457911Z","submitted_at":"2019-05-01T17:57:26Z","title":"Similarity of Neural Network Representations Revisited","version":4},"cited_work":{"arxiv_id":"1905.00414","doi":"10.48550/arxiv.1905.00414","metadata_source":"pith","pith_arxiv_id":"1905.00414","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Similarity of Neural Network Representations Revisited","venue":"cs.LG","work_id":"0879bfbc-f331-4049-bce8-9db54ae74fc4","year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"cited_paper":"/paper/1905.00414","citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:03405eb2ebbf6fdf9be2d432101d186ceec04818bcc57419e33663ae3fd1c42b","observation_id":"b8b32f8b-7909-47b4-a758-74c4c0f5df66","resolution":{"observed_at":"2026-07-03T20:08:55.686402Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-06-01T22:57:46.874929+00:00","source":"crossref_status_cache"},{"observed_at":"2026-06-01T22:57:46.874929+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-27T01:42:23.454308Z","title":"MacDonald, P","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:41100013ba9cc694b937496546835d995345e4b9470441d45463fdd53d8f29c9","observation_id":"05b232b6-b249-4d23-9945-a385ce492d59","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Gp+: A python library for kernel-based learning via gaussian processes.Advances in Engineering Software, 195:103686, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:dfefb6e08afeef556c6344313eabdbe2a4f785ac5697bc9432fb43fbb70179c5","observation_id":"4c2fcfcf-838f-4861-a6b5-bf9ab8e9f4a2","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:476388bf02d62ca3c727ba0fa326e648b78dae0787531d366cdedcc8a5a317d7","observation_id":"287155b4-1c29-4907-8d2b-534896eecffe","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"A mini-batch method for solving nonlinear pdes with gaussian processes, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:a576b2ef0536d4915631c8e51e4b62b971b8fa9d079139c2ff8c159e2ad03b0a","observation_id":"c03f5e83-cc9c-40dd-b03e-203e3cf38bd5","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Gomez, Łukasz Kaiser, and Illia Polosukhin","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:49d77e354c351c8bc2e76aded20ce368699ecbfc7a8b7c3f228b2e39a0d56b32","observation_id":"4844ba6d-154e-44a6-bbfd-8752712ef7a9","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Deep residual learning for image recognition, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:9f144dc35356cf8feb0c7c292567b4ac4e79e3175880955f4f27cb108fce8fac","observation_id":"8ac79d3c-8a4c-4aae-843a-24dfbbf3d5b6","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Gaussian error linear units (gelus), 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:a9d2e711f00ae226c15aa3921accf687acf94c45c51dbf06240600a75a8056d5","observation_id":"05c5ab5b-2a29-4b4f-8e6a-4adedfcd6103","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Decoupled weight decay regularization, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:59adacf759a2af86eb28500162f8290813be1fd8319538f91e338320e0190417","observation_id":"72275fd2-b64e-4087-83a0-3db33e10dd0d","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:f264632d1aa1c067ce104b8c1024e73c28ad00bb223b98b54cd42e32aa94dcf6","observation_id":"267a347e-9d8b-4582-8c28-68ae56244217","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Learning three-dimensional flow for interactive aerody- namic design.ACM Trans","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:3a669c3e01d5cd47bb7ec9387c108ad1f702470f4cc558307dad57a73b3d9616","observation_id":"5eedb604-1cde-4cd1-a758-34e6e9c06f23","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:5275472bcb84e5c758c643e5fe2124c316fb92019c9faa385a009822f1a4652a","observation_id":"ba36db3b-2ade-4d51-a6c8-bc19db5f7d9a","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","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":"2026-06-27T01:42:23.454308Z","title":"Specifically, instead of learning the map G† directly (which outputs an infinite-dimensional function), we learn the evaluation functional associated with the operator","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:8e6a1e59e009e4c2cb8de3eb0ad308a9b5d029cd1dc736a93f963997c99a9caa","observation_id":"634d9cca-c4f6-41d8-8190-18a3c37bbd43","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-06-27T01:42:23.454308Z","title":"The architecture is configured based on the original setup to achieve near state-of-the-art predictive accuracy","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-06-27T01:42:23.454308Z"},"links":{"citing_paper":"/paper/2606.17513"},"observation_digest":"sha256:37913b93347c540dec204de0cc4a7a61eae9232df9bbb68eb78f831ca4f0764c","observation_id":"9a506e50-bf9b-4ae3-bfd3-7bc7a40ca3dd","resolution":{"observed_at":"2026-06-27T01:42:23.454308Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.17513","last_updated":"2026-06-16T04:46:17Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-18T02:15:27.380674Z","submitted_at":"2026-06-16T04:46:17Z","title":"Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning"},"reference_resolution":{"displayed":66,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":60,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":66},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 0 inbound Pith citation observations for arXiv:2606.17513."}