{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XVU5G6PIZ2K6AQIVS2TJQ2FJQG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2493b2ca65a6dbecb42bef42021f1fb36fe6b7ca05c8a8fd4f4941e9f91c6328","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-30T11:41:58Z","title_canon_sha256":"ecd750eb4665cb8f7479e9b43ddf4f89c876883548f3f32b156ab35cd51e839d"},"schema_version":"1.0","source":{"id":"2409.20206","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.20206","created_at":"2026-07-05T11:08:01Z"},{"alias_kind":"arxiv_version","alias_value":"2409.20206v4","created_at":"2026-07-05T11:08:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20206","created_at":"2026-07-05T11:08:01Z"},{"alias_kind":"pith_short_12","alias_value":"XVU5G6PIZ2K6","created_at":"2026-07-05T11:08:01Z"},{"alias_kind":"pith_short_16","alias_value":"XVU5G6PIZ2K6AQIV","created_at":"2026-07-05T11:08:01Z"},{"alias_kind":"pith_short_8","alias_value":"XVU5G6PI","created_at":"2026-07-05T11:08:01Z"}],"graph_snapshots":[{"event_id":"sha256:70d0e574e3626635224a2260c5a46d169bba635dfe1ce7bff46ad5f00f9f4c8a","target":"graph","created_at":"2026-07-05T11:08:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.20206/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal solutions. We introduce SetPINNs, a framework that effectively captures local dependencies. With a finite element-inspired sampling scheme, we partition the domain into sets to model local dependencies while simultaneously enforcing physical laws. We provide a rigorous theoretical analysis showing that SetPINNs yield unbiased, lower-variance estimates of residual ene","authors_text":"Fabian Jirasek, Frank Rhein, Marius Kloft, Mayank Nagda, Phil Ostheimer, Sophie Fellenz, Stephan Mandt, Thomas Specht","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-30T11:41:58Z","title":"SetPINNs: Set-based Physics-informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20206","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f878595bfb8229dce3e1361956c1b909a0a5d2c30db01d801dda2e33e70fa888","target":"record","created_at":"2026-07-05T11:08:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2493b2ca65a6dbecb42bef42021f1fb36fe6b7ca05c8a8fd4f4941e9f91c6328","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-09-30T11:41:58Z","title_canon_sha256":"ecd750eb4665cb8f7479e9b43ddf4f89c876883548f3f32b156ab35cd51e839d"},"schema_version":"1.0","source":{"id":"2409.20206","kind":"arxiv","version":4}},"canonical_sha256":"bd69d379e8ce95e0411596a69868a9818178920e1789a70d9a74a6d441c89c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd69d379e8ce95e0411596a69868a9818178920e1789a70d9a74a6d441c89c48","first_computed_at":"2026-07-05T11:08:01.302014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:01.302014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwJl2c8N4YK/zdU/rfHQIE05Rs0BJFfpe/La1jpAxyDagB6WwoGD56hp5RgGIBN1VaTj4Q/eNw+oS/hLLC5tAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:01.302486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.20206","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f878595bfb8229dce3e1361956c1b909a0a5d2c30db01d801dda2e33e70fa888","sha256:70d0e574e3626635224a2260c5a46d169bba635dfe1ce7bff46ad5f00f9f4c8a"],"state_sha256":"e2c61b06578e859ac0239fea5fe89e500460d4be7e03aa78140ab58593556780"}