{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5K3RNSZ7IWHISTQOM4W5PIJPAI","short_pith_number":"pith:5K3RNSZ7","canonical_record":{"source":{"id":"2402.00531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-01T11:58:28Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d499358a9eee4b1b34605a97b6c374ddbe55d7caeb8c4b2e7d78736856787b82","abstract_canon_sha256":"16c24c4b9ee6a282a4d217dcfd78bf296ad885927115cb882600b661a5160bcc"},"schema_version":"1.0"},"canonical_sha256":"eab716cb3f458e894e0e672dd7a12f020b0765c53dd2bd529f2972736268dba8","source":{"kind":"arxiv","id":"2402.00531","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.00531","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"2402.00531v1","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.00531","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"5K3RNSZ7IWHI","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_16","alias_value":"5K3RNSZ7IWHISTQO","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_8","alias_value":"5K3RNSZ7","created_at":"2026-07-05T07:40:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5K3RNSZ7IWHISTQOM4W5PIJPAI","target":"record","payload":{"canonical_record":{"source":{"id":"2402.00531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-01T11:58:28Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d499358a9eee4b1b34605a97b6c374ddbe55d7caeb8c4b2e7d78736856787b82","abstract_canon_sha256":"16c24c4b9ee6a282a4d217dcfd78bf296ad885927115cb882600b661a5160bcc"},"schema_version":"1.0"},"canonical_sha256":"eab716cb3f458e894e0e672dd7a12f020b0765c53dd2bd529f2972736268dba8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:40:13.086142Z","signature_b64":"TW2Eal/0TCosF0BSEt+HbnEH3r1fJuj7YjspOW2ry/SPFdf2xk22bMFi6FlBl+XlKwVrsCIgGCXpvxm7G0WACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eab716cb3f458e894e0e672dd7a12f020b0765c53dd2bd529f2972736268dba8","last_reissued_at":"2026-07-05T07:40:13.085659Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:40:13.085659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.00531","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:40:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ay082atZQFPxjVsE6optZmScxAFwLfB4YIjKkRBOV6WZpbaMfF449WMxUV6cnQ0/fVmqq/qHD/plFtcklKmCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T11:10:16.261807Z"},"content_sha256":"f1b0703a4286b810195e115a38cbc1845728e63ac0c0bf8c2b03cf0400fbecf6","schema_version":"1.0","event_id":"sha256:f1b0703a4286b810195e115a38cbc1845728e63ac0c0bf8c2b03cf0400fbecf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5K3RNSZ7IWHISTQOM4W5PIJPAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preconditioning for Physics-Informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Chang Su, Hang Su, Jiachen Yao, Jun Zhu, Songming Liu, Youjia Wu, Zhongkai Hao","submitted_at":"2024-02-01T11:58:28Z","abstract_excerpt":"Physics-informed neural networks (PINNs) have shown promise in solving various partial differential equations (PDEs). However, training pathologies have negatively affected the convergence and prediction accuracy of PINNs, which further limits their practical applications. In this paper, we propose to use condition number as a metric to diagnose and mitigate the pathologies in PINNs. Inspired by classical numerical analysis, where the condition number measures sensitivity and stability, we highlight its pivotal role in the training dynamics of PINNs. We prove theorems to reveal how condition n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.00531","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.00531/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:40:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+J7ujMn/GpP5KlIJQqY3lbcw7UfAHNJloEHnw4deHmufIWeeyx8I/+ThUN9jpj65G4QeFX+UValmBD03lPnyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T11:10:16.262175Z"},"content_sha256":"093960459c8081eeaf5d6e337b94c7b47de6541a1165c458fa5dc8fd72759764","schema_version":"1.0","event_id":"sha256:093960459c8081eeaf5d6e337b94c7b47de6541a1165c458fa5dc8fd72759764"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/bundle.json","state_url":"https://pith.science/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-17T11:10:16Z","links":{"resolver":"https://pith.science/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI","bundle":"https://pith.science/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/bundle.json","state":"https://pith.science/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5K3RNSZ7IWHISTQOM4W5PIJPAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5K3RNSZ7IWHISTQOM4W5PIJPAI","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":"16c24c4b9ee6a282a4d217dcfd78bf296ad885927115cb882600b661a5160bcc","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-01T11:58:28Z","title_canon_sha256":"d499358a9eee4b1b34605a97b6c374ddbe55d7caeb8c4b2e7d78736856787b82"},"schema_version":"1.0","source":{"id":"2402.00531","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.00531","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"2402.00531v1","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.00531","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"5K3RNSZ7IWHI","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_16","alias_value":"5K3RNSZ7IWHISTQO","created_at":"2026-07-05T07:40:13Z"},{"alias_kind":"pith_short_8","alias_value":"5K3RNSZ7","created_at":"2026-07-05T07:40:13Z"}],"graph_snapshots":[{"event_id":"sha256:093960459c8081eeaf5d6e337b94c7b47de6541a1165c458fa5dc8fd72759764","target":"graph","created_at":"2026-07-05T07:40:13Z","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/2402.00531/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural networks (PINNs) have shown promise in solving various partial differential equations (PDEs). However, training pathologies have negatively affected the convergence and prediction accuracy of PINNs, which further limits their practical applications. In this paper, we propose to use condition number as a metric to diagnose and mitigate the pathologies in PINNs. Inspired by classical numerical analysis, where the condition number measures sensitivity and stability, we highlight its pivotal role in the training dynamics of PINNs. We prove theorems to reveal how condition n","authors_text":"Chang Su, Hang Su, Jiachen Yao, Jun Zhu, Songming Liu, Youjia Wu, Zhongkai Hao","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-01T11:58:28Z","title":"Preconditioning for Physics-Informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.00531","kind":"arxiv","version":1},"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:f1b0703a4286b810195e115a38cbc1845728e63ac0c0bf8c2b03cf0400fbecf6","target":"record","created_at":"2026-07-05T07:40:13Z","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":"16c24c4b9ee6a282a4d217dcfd78bf296ad885927115cb882600b661a5160bcc","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-01T11:58:28Z","title_canon_sha256":"d499358a9eee4b1b34605a97b6c374ddbe55d7caeb8c4b2e7d78736856787b82"},"schema_version":"1.0","source":{"id":"2402.00531","kind":"arxiv","version":1}},"canonical_sha256":"eab716cb3f458e894e0e672dd7a12f020b0765c53dd2bd529f2972736268dba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eab716cb3f458e894e0e672dd7a12f020b0765c53dd2bd529f2972736268dba8","first_computed_at":"2026-07-05T07:40:13.085659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:40:13.085659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TW2Eal/0TCosF0BSEt+HbnEH3r1fJuj7YjspOW2ry/SPFdf2xk22bMFi6FlBl+XlKwVrsCIgGCXpvxm7G0WACg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:40:13.086142Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.00531","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1b0703a4286b810195e115a38cbc1845728e63ac0c0bf8c2b03cf0400fbecf6","sha256:093960459c8081eeaf5d6e337b94c7b47de6541a1165c458fa5dc8fd72759764"],"state_sha256":"1b85f49fd9a259b7c2c5c0f339cef00abe603234edfa1ef8a03585c076806b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IniUfAjQZdfcUt81CvrVnZ3PwYZUPSc39/blGZTCA0rKzS6di74Th8TsFhvWUP+NMdQ2/dpreSp1xDddXom8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T11:10:16.264370Z","bundle_sha256":"a069d075e097c0f220e60b75ddbe6e1d2acdad8d4b9a8a2c236c1b4a97843150"}}