{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NDDKCIKHOMCNPB6PU6CNQNDCW3","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":"decd50b02c369f3923ef6630f363c7303a6929d17d1e0939f528ad7cd6c095b1","cross_cats_sorted":["physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2020-06-21T20:01:13Z","title_canon_sha256":"68dc51997f85e9d521c7a1d9b047240a8dd2a593691c3435585e3e6b5303d6c8"},"schema_version":"1.0","source":{"id":"2006.11894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.11894","created_at":"2026-07-05T01:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2006.11894v1","created_at":"2026-07-05T01:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.11894","created_at":"2026-07-05T01:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"NDDKCIKHOMCN","created_at":"2026-07-05T01:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"NDDKCIKHOMCNPB6P","created_at":"2026-07-05T01:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"NDDKCIKH","created_at":"2026-07-05T01:11:54Z"}],"graph_snapshots":[{"event_id":"sha256:f47662c32ec4b9400fdd5c089ccc21b041a0ab09cb9f1a76a0b787a3920f3057","target":"graph","created_at":"2026-07-05T01:11:54Z","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/2006.11894/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale, propagating and oscillatory nature of its solutions, and it is unclear how well they perform in this setting. We use a deep neural network to learn solutions of the wave equation, using the wave equation and a boundary condition as direct constraints in the loss function when training the network. We test the approach by solving the 2D acoustic wave equatio","authors_text":"Andrew Markham, Ben Moseley, Tarje Nissen-Meyer","cross_cats":["physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2020-06-21T20:01:13Z","title":"Solving the wave equation with physics-informed deep learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.11894","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":"sha256:97261c6a112904541ba0f2e4b8a35074bc11ed7886ca76b7228b04b34633fc13","target":"record","created_at":"2026-07-05T01:11:54Z","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":"decd50b02c369f3923ef6630f363c7303a6929d17d1e0939f528ad7cd6c095b1","cross_cats_sorted":["physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2020-06-21T20:01:13Z","title_canon_sha256":"68dc51997f85e9d521c7a1d9b047240a8dd2a593691c3435585e3e6b5303d6c8"},"schema_version":"1.0","source":{"id":"2006.11894","kind":"arxiv","version":1}},"canonical_sha256":"68c6a121477304d787cfa784d83462b6e5d3592bc03ea1887e8ee2746b0adb9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68c6a121477304d787cfa784d83462b6e5d3592bc03ea1887e8ee2746b0adb9f","first_computed_at":"2026-07-05T01:11:54.718926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:11:54.718926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3fjNaCeC0S2rzBZcyCILOQ1pj65r/s+6/cqX+pu+iJ8DjiX/cXG2lPeahMCNgMjiCUPDOkVN//0svKAki/aWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:11:54.719343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.11894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97261c6a112904541ba0f2e4b8a35074bc11ed7886ca76b7228b04b34633fc13","sha256:f47662c32ec4b9400fdd5c089ccc21b041a0ab09cb9f1a76a0b787a3920f3057"],"state_sha256":"9ee3a39a109e9045b6711fecdf7020fae8f5603400ce19a5c45013400d11d86c"}