{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:C7COLRRFTERGRHLLBXFBCMGRQF","short_pith_number":"pith:C7COLRRF","canonical_record":{"source":{"id":"2009.04544","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-07T04:07:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"187ec1fffe14ec7c6405b50362a42005160c1e971c7094708fb69e67cfb90fd3","abstract_canon_sha256":"8ade1428f4f6a049056f9b1f4e649e22ac1f15fdc1d8b32a883c6a70a6acaa7c"},"schema_version":"1.0"},"canonical_sha256":"17c4e5c6259922689d6b0dca1130d18148ee8aa1dafd86eed48611c5234dcdac","source":{"kind":"arxiv","id":"2009.04544","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.04544","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"2009.04544v5","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.04544","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"C7COLRRFTERG","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_16","alias_value":"C7COLRRFTERGRHLL","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_8","alias_value":"C7COLRRF","created_at":"2026-07-05T08:33:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:C7COLRRFTERGRHLLBXFBCMGRQF","target":"record","payload":{"canonical_record":{"source":{"id":"2009.04544","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-07T04:07:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"187ec1fffe14ec7c6405b50362a42005160c1e971c7094708fb69e67cfb90fd3","abstract_canon_sha256":"8ade1428f4f6a049056f9b1f4e649e22ac1f15fdc1d8b32a883c6a70a6acaa7c"},"schema_version":"1.0"},"canonical_sha256":"17c4e5c6259922689d6b0dca1130d18148ee8aa1dafd86eed48611c5234dcdac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:58.992832Z","signature_b64":"osI252ZjfD2+mFLrgB1kkCm0yriTyXZwC7LS+vMhYVByquhC7KnQPM0KE9G3QsoCpfH7T4ul4jO9dS8V9IVyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17c4e5c6259922689d6b0dca1130d18148ee8aa1dafd86eed48611c5234dcdac","last_reissued_at":"2026-07-05T08:33:58.992377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:58.992377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.04544","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4wJpkwdjtS/X71AZUbuoucAazPfrQjcvFHLIrbd4FQ1dSl2cDUhs4rBTKgwKQUPeaor0lBgBTAlzFKyhp6zAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:21:01.653770Z"},"content_sha256":"5e574d049af060ea1e7e3d68e0f31da74a3c39687f9000fc9e0b9aa9f391dfa3","schema_version":"1.0","event_id":"sha256:5e574d049af060ea1e7e3d68e0f31da74a3c39687f9000fc9e0b9aa9f391dfa3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:C7COLRRFTERGRHLLBXFBCMGRQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Levi McClenny, Ulisses Braga-Neto","submitted_at":"2020-09-07T04:07:52Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive procedures are needed to force the neural network to fit accurately the stubborn spots in the solution of \"stiff\" PDEs. In this paper, we propose a fundamentally new way to train PINNs adaptively, where the adaptation weights are fully trainable and applied to each training point individually, so the neural network learns autonomously which regions of the solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.04544","kind":"arxiv","version":5},"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/2009.04544/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":"2026-07-05T08:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgpKqPwdadXMZWbPxeKzmVVWE1lDs0hURrI4lyH5riIixPUqzV9ND2XLpaET96clwFClis6sElpQTBzUkwoMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:21:01.654141Z"},"content_sha256":"d3257ef2b5a06b5523ebed25671e28d704d06070bdadfe57915b9fd329411db7","schema_version":"1.0","event_id":"sha256:d3257ef2b5a06b5523ebed25671e28d704d06070bdadfe57915b9fd329411db7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7COLRRFTERGRHLLBXFBCMGRQF/bundle.json","state_url":"https://pith.science/pith/C7COLRRFTERGRHLLBXFBCMGRQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7COLRRFTERGRHLLBXFBCMGRQF/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":"2026-07-07T10:21:01Z","links":{"resolver":"https://pith.science/pith/C7COLRRFTERGRHLLBXFBCMGRQF","bundle":"https://pith.science/pith/C7COLRRFTERGRHLLBXFBCMGRQF/bundle.json","state":"https://pith.science/pith/C7COLRRFTERGRHLLBXFBCMGRQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7COLRRFTERGRHLLBXFBCMGRQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:C7COLRRFTERGRHLLBXFBCMGRQF","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":"8ade1428f4f6a049056f9b1f4e649e22ac1f15fdc1d8b32a883c6a70a6acaa7c","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-07T04:07:52Z","title_canon_sha256":"187ec1fffe14ec7c6405b50362a42005160c1e971c7094708fb69e67cfb90fd3"},"schema_version":"1.0","source":{"id":"2009.04544","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.04544","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"2009.04544v5","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.04544","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"C7COLRRFTERG","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_16","alias_value":"C7COLRRFTERGRHLL","created_at":"2026-07-05T08:33:58Z"},{"alias_kind":"pith_short_8","alias_value":"C7COLRRF","created_at":"2026-07-05T08:33:58Z"}],"graph_snapshots":[{"event_id":"sha256:d3257ef2b5a06b5523ebed25671e28d704d06070bdadfe57915b9fd329411db7","target":"graph","created_at":"2026-07-05T08:33:58Z","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/2009.04544/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive procedures are needed to force the neural network to fit accurately the stubborn spots in the solution of \"stiff\" PDEs. In this paper, we propose a fundamentally new way to train PINNs adaptively, where the adaptation weights are fully trainable and applied to each training point individually, so the neural network learns autonomously which regions of the solu","authors_text":"Levi McClenny, Ulisses Braga-Neto","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-07T04:07:52Z","title":"Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.04544","kind":"arxiv","version":5},"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":"sha256:5e574d049af060ea1e7e3d68e0f31da74a3c39687f9000fc9e0b9aa9f391dfa3","target":"record","created_at":"2026-07-05T08:33:58Z","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":"8ade1428f4f6a049056f9b1f4e649e22ac1f15fdc1d8b32a883c6a70a6acaa7c","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-07T04:07:52Z","title_canon_sha256":"187ec1fffe14ec7c6405b50362a42005160c1e971c7094708fb69e67cfb90fd3"},"schema_version":"1.0","source":{"id":"2009.04544","kind":"arxiv","version":5}},"canonical_sha256":"17c4e5c6259922689d6b0dca1130d18148ee8aa1dafd86eed48611c5234dcdac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17c4e5c6259922689d6b0dca1130d18148ee8aa1dafd86eed48611c5234dcdac","first_computed_at":"2026-07-05T08:33:58.992377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:58.992377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"osI252ZjfD2+mFLrgB1kkCm0yriTyXZwC7LS+vMhYVByquhC7KnQPM0KE9G3QsoCpfH7T4ul4jO9dS8V9IVyDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:58.992832Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.04544","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e574d049af060ea1e7e3d68e0f31da74a3c39687f9000fc9e0b9aa9f391dfa3","sha256:d3257ef2b5a06b5523ebed25671e28d704d06070bdadfe57915b9fd329411db7"],"state_sha256":"7d1c50ef029acc5821124029e8f5bfc932a2bfa8507e473a250348bfe6b62e0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Duv7mCJLqXk1NSk/CEshuxj4jrHw0gaAS6HZj2/NJVsGAlok+lFey1brBWAJMRh2J606G6nb+qVcH3nfY6RVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:21:01.656062Z","bundle_sha256":"dd3d6322d74027224daf07fc45f4a5cf68f262fc9e37200b086050ec397e7d5c"}}