{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LVFUENAYWN26LBVN2NLXPQSRRM","short_pith_number":"pith:LVFUENAY","canonical_record":{"source":{"id":"2410.01599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-02T14:38:37Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"e18a3401eacfdf0555fd505c5f5d1e01579598ca6d1b4d38d791e5a22d8b4059","abstract_canon_sha256":"f864ea010e2adb5ed575b6be9ec3bb3405bd8c448ff7b32b10c5c07b6a33f2e4"},"schema_version":"1.0"},"canonical_sha256":"5d4b423418b375e586add35777c2518b3865da6e9534351f4776387316260cdf","source":{"kind":"arxiv","id":"2410.01599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.01599","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"arxiv_version","alias_value":"2410.01599v1","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.01599","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_12","alias_value":"LVFUENAYWN26","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_16","alias_value":"LVFUENAYWN26LBVN","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_8","alias_value":"LVFUENAY","created_at":"2026-07-05T09:14:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LVFUENAYWN26LBVN2NLXPQSRRM","target":"record","payload":{"canonical_record":{"source":{"id":"2410.01599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-02T14:38:37Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"e18a3401eacfdf0555fd505c5f5d1e01579598ca6d1b4d38d791e5a22d8b4059","abstract_canon_sha256":"f864ea010e2adb5ed575b6be9ec3bb3405bd8c448ff7b32b10c5c07b6a33f2e4"},"schema_version":"1.0"},"canonical_sha256":"5d4b423418b375e586add35777c2518b3865da6e9534351f4776387316260cdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:14:49.816668Z","signature_b64":"fn9zxPzkYa257uvQg82jkm3UaiGZ4OHEiEONsLEQYN+Y9sBopNllbmwNWE3ZOhrvHZhqDSBqPwjz3Kz5q7n6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d4b423418b375e586add35777c2518b3865da6e9534351f4776387316260cdf","last_reissued_at":"2026-07-05T09:14:49.816259Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:14:49.816259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.01599","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":"2026-07-05T09:14:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JLSGJ+mS+pzLJoVcHXKfMoTiSHVJOOoNRhxu2A63ZgE3h2Bv54ht3EtXFhUTmp368fdlZ4qo5MIncxR9hJiXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T18:43:25.456878Z"},"content_sha256":"31c457511683ab6015afd2ef1c81db1c0dc875cdd09cbce35524532126ecad53","schema_version":"1.0","event_id":"sha256:31c457511683ab6015afd2ef1c81db1c0dc875cdd09cbce35524532126ecad53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LVFUENAYWN26LBVN2NLXPQSRRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Model Discovery Using Domain Decomposition and PINNs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Heinlein, Cordula Reisch, Tirtho S. Saha","submitted_at":"2024-10-02T14:38:37Z","abstract_excerpt":"We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.01599","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/2410.01599/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":"2026-07-05T09:14:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYENlQEA0oRODxGVX5rx9Z/1WBPMwbRlKw6SChREW6CNRCkPEdyy5q2VWD2V6bwizsnIYan2sAKHWUkzW0aKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T18:43:25.457436Z"},"content_sha256":"bba388625428b73b068014eb2d5febfcf27c67b8eac1cd9e2c3b8651e46fb393","schema_version":"1.0","event_id":"sha256:bba388625428b73b068014eb2d5febfcf27c67b8eac1cd9e2c3b8651e46fb393"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVFUENAYWN26LBVN2NLXPQSRRM/bundle.json","state_url":"https://pith.science/pith/LVFUENAYWN26LBVN2NLXPQSRRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVFUENAYWN26LBVN2NLXPQSRRM/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":"2026-07-31T18:43:25Z","links":{"resolver":"https://pith.science/pith/LVFUENAYWN26LBVN2NLXPQSRRM","bundle":"https://pith.science/pith/LVFUENAYWN26LBVN2NLXPQSRRM/bundle.json","state":"https://pith.science/pith/LVFUENAYWN26LBVN2NLXPQSRRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVFUENAYWN26LBVN2NLXPQSRRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LVFUENAYWN26LBVN2NLXPQSRRM","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":"f864ea010e2adb5ed575b6be9ec3bb3405bd8c448ff7b32b10c5c07b6a33f2e4","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-02T14:38:37Z","title_canon_sha256":"e18a3401eacfdf0555fd505c5f5d1e01579598ca6d1b4d38d791e5a22d8b4059"},"schema_version":"1.0","source":{"id":"2410.01599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.01599","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"arxiv_version","alias_value":"2410.01599v1","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.01599","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_12","alias_value":"LVFUENAYWN26","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_16","alias_value":"LVFUENAYWN26LBVN","created_at":"2026-07-05T09:14:49Z"},{"alias_kind":"pith_short_8","alias_value":"LVFUENAY","created_at":"2026-07-05T09:14:49Z"}],"graph_snapshots":[{"event_id":"sha256:bba388625428b73b068014eb2d5febfcf27c67b8eac1cd9e2c3b8651e46fb393","target":"graph","created_at":"2026-07-05T09:14:49Z","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/2410.01599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach com","authors_text":"Alexander Heinlein, Cordula Reisch, Tirtho S. Saha","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-02T14:38:37Z","title":"Towards Model Discovery Using Domain Decomposition and PINNs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.01599","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":"sha256:31c457511683ab6015afd2ef1c81db1c0dc875cdd09cbce35524532126ecad53","target":"record","created_at":"2026-07-05T09:14:49Z","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":"f864ea010e2adb5ed575b6be9ec3bb3405bd8c448ff7b32b10c5c07b6a33f2e4","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-02T14:38:37Z","title_canon_sha256":"e18a3401eacfdf0555fd505c5f5d1e01579598ca6d1b4d38d791e5a22d8b4059"},"schema_version":"1.0","source":{"id":"2410.01599","kind":"arxiv","version":1}},"canonical_sha256":"5d4b423418b375e586add35777c2518b3865da6e9534351f4776387316260cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d4b423418b375e586add35777c2518b3865da6e9534351f4776387316260cdf","first_computed_at":"2026-07-05T09:14:49.816259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:14:49.816259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fn9zxPzkYa257uvQg82jkm3UaiGZ4OHEiEONsLEQYN+Y9sBopNllbmwNWE3ZOhrvHZhqDSBqPwjz3Kz5q7n6Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:14:49.816668Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.01599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31c457511683ab6015afd2ef1c81db1c0dc875cdd09cbce35524532126ecad53","sha256:bba388625428b73b068014eb2d5febfcf27c67b8eac1cd9e2c3b8651e46fb393"],"state_sha256":"35d1f0fca197e9ca6a0c2421761f68395137d8b491b344d1fdbca981cfd4fdc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q76apXbLasFcBg32b35NGgp+97b0qpQgUGH626OBzdT+WreEgQ0jMLpnTl1lC362TL7SWOd2iA3N2Z+2daDXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T18:43:25.463278Z","bundle_sha256":"4eadd7d0a3bf367c391afc878e5781f09ab011dbf702c35cdcf9fd12b3fbca3d"}}