{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LHZGTIR42DEAADCXZZJQIUPV3Y","short_pith_number":"pith:LHZGTIR4","canonical_record":{"source":{"id":"2104.10013","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2021-04-20T17:41:54Z","cross_cats_sorted":[],"title_canon_sha256":"1d83616342a1222c7d9c036c676ca03f5b65e834cf328c4fcd40c51330d78be9","abstract_canon_sha256":"de46c783626e4dcaaf1546e9badc8c81bf8652f28868372bbd85735284d60e31"},"schema_version":"1.0"},"canonical_sha256":"59f269a23cd0c8000c57ce530451f5de122c70e2530012e125d2807ec62d03dc","source":{"kind":"arxiv","id":"2104.10013","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.10013","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"2104.10013v3","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.10013","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"LHZGTIR42DEA","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHZGTIR42DEAADCX","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHZGTIR4","created_at":"2026-07-05T03:12:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LHZGTIR42DEAADCXZZJQIUPV3Y","target":"record","payload":{"canonical_record":{"source":{"id":"2104.10013","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2021-04-20T17:41:54Z","cross_cats_sorted":[],"title_canon_sha256":"1d83616342a1222c7d9c036c676ca03f5b65e834cf328c4fcd40c51330d78be9","abstract_canon_sha256":"de46c783626e4dcaaf1546e9badc8c81bf8652f28868372bbd85735284d60e31"},"schema_version":"1.0"},"canonical_sha256":"59f269a23cd0c8000c57ce530451f5de122c70e2530012e125d2807ec62d03dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:12:38.575397Z","signature_b64":"IVd9C9o6mzbqVrjnE5mX31aoxddPAwCh3YjO8Xoh4HHkFAKUUNBUDIqHghSKp0cD2yHza3RWZ9dofuTLvfCPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59f269a23cd0c8000c57ce530451f5de122c70e2530012e125d2807ec62d03dc","last_reissued_at":"2026-07-05T03:12:38.575004Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:12:38.575004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.10013","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+0YZkoieyHju6eqYG9zoT+vc6aoyuTddQ+MaJAWIFW9RwUxiYwmZJvk/OsG6e303gjf9Te26cX43m8t2ARpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:51:35.850185Z"},"content_sha256":"bc4d2179280d039f711d5a8594f780b4cecf7c81fef16978538cab7ca44efc30","schema_version":"1.0","event_id":"sha256:bc4d2179280d039f711d5a8594f780b4cecf7c81fef16978538cab7ca44efc30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LHZGTIR42DEAADCXZZJQIUPV3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel Physics-Informed Neural Networks via Domain Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Ameya D. Jagtap, George Em Karniadakis, Khemraj Shukla","submitted_at":"2021-04-20T17:41:54Z","abstract_excerpt":"We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.10013","kind":"arxiv","version":3},"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/2104.10013/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":"2026-07-05T03:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTi+Unr2j0jqof3D9yoIePxdA3mX7RbYIIaOQpnM4Fssy5qwGc+Gt9mhJ9kBu2VomCtUUDovuHgRFBf/HpnfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:51:35.850563Z"},"content_sha256":"19d6209159156d69dd553c26cea1779cc1e23dfe49958614d75ededb87afc40b","schema_version":"1.0","event_id":"sha256:19d6209159156d69dd553c26cea1779cc1e23dfe49958614d75ededb87afc40b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/bundle.json","state_url":"https://pith.science/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/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":"2026-08-21T19:51:35Z","links":{"resolver":"https://pith.science/pith/LHZGTIR42DEAADCXZZJQIUPV3Y","bundle":"https://pith.science/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/bundle.json","state":"https://pith.science/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHZGTIR42DEAADCXZZJQIUPV3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LHZGTIR42DEAADCXZZJQIUPV3Y","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":"de46c783626e4dcaaf1546e9badc8c81bf8652f28868372bbd85735284d60e31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2021-04-20T17:41:54Z","title_canon_sha256":"1d83616342a1222c7d9c036c676ca03f5b65e834cf328c4fcd40c51330d78be9"},"schema_version":"1.0","source":{"id":"2104.10013","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.10013","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"2104.10013v3","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.10013","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"LHZGTIR42DEA","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHZGTIR42DEAADCX","created_at":"2026-07-05T03:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHZGTIR4","created_at":"2026-07-05T03:12:38Z"}],"graph_snapshots":[{"event_id":"sha256:19d6209159156d69dd553c26cea1779cc1e23dfe49958614d75ededb87afc40b","target":"graph","created_at":"2026-07-05T03:12:38Z","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/2104.10013/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed w","authors_text":"Ameya D. Jagtap, George Em Karniadakis, Khemraj Shukla","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2021-04-20T17:41:54Z","title":"Parallel Physics-Informed Neural Networks via Domain Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.10013","kind":"arxiv","version":3},"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:bc4d2179280d039f711d5a8594f780b4cecf7c81fef16978538cab7ca44efc30","target":"record","created_at":"2026-07-05T03:12:38Z","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":"de46c783626e4dcaaf1546e9badc8c81bf8652f28868372bbd85735284d60e31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DC","submitted_at":"2021-04-20T17:41:54Z","title_canon_sha256":"1d83616342a1222c7d9c036c676ca03f5b65e834cf328c4fcd40c51330d78be9"},"schema_version":"1.0","source":{"id":"2104.10013","kind":"arxiv","version":3}},"canonical_sha256":"59f269a23cd0c8000c57ce530451f5de122c70e2530012e125d2807ec62d03dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59f269a23cd0c8000c57ce530451f5de122c70e2530012e125d2807ec62d03dc","first_computed_at":"2026-07-05T03:12:38.575004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:12:38.575004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVd9C9o6mzbqVrjnE5mX31aoxddPAwCh3YjO8Xoh4HHkFAKUUNBUDIqHghSKp0cD2yHza3RWZ9dofuTLvfCPBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:12:38.575397Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.10013","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc4d2179280d039f711d5a8594f780b4cecf7c81fef16978538cab7ca44efc30","sha256:19d6209159156d69dd553c26cea1779cc1e23dfe49958614d75ededb87afc40b"],"state_sha256":"16d90ecf9d787c291bf5ca53d44f4e552afaf291f247a4f74f104a87b713a880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ja+adYs5ZVjYZld7n8fOHgdn9lmXdMdiHHwlCSZhq15jZwUt2y2IVkJ4gY8Un7ssPJbDl4OGmWkqJa6eUdpWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:51:35.853120Z","bundle_sha256":"adc76aaa4ab5e60b3179fc1fd8999de803ebba0f09c3aec5fda4d24283ec7550"}}