{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BJV3WGTXG33HTGGDLQ2MPJIDEA","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":"3e00bf11883fa427c7a9618a8733510c9eba242644e203a87d3f31a66268e6f4","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2021-01-15T15:43:41Z","title_canon_sha256":"ee7515229dea512f5154fc2e2a93649aa28fcad781548ff843353e92e3d22c55"},"schema_version":"1.0","source":{"id":"2101.06182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.06182","created_at":"2026-07-05T02:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"2101.06182v2","created_at":"2026-07-05T02:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.06182","created_at":"2026-07-05T02:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"BJV3WGTXG33H","created_at":"2026-07-05T02:07:34Z"},{"alias_kind":"pith_short_16","alias_value":"BJV3WGTXG33HTGGD","created_at":"2026-07-05T02:07:34Z"},{"alias_kind":"pith_short_8","alias_value":"BJV3WGTX","created_at":"2026-07-05T02:07:34Z"}],"graph_snapshots":[{"event_id":"sha256:5b35020aeffe73d23722e81451f8a75b30775c7ab93dec3afed7fb93ef06066f","target":"graph","created_at":"2026-07-05T02:07:34Z","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/2101.06182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in the PDE solution, e.g., in applications like turbulence, combustion, and shock propagation. Numerical approximation also requires knowing the PDE in order to construct problem-specific discretizations. Systematically deriving such solution-adaptive discrete operators, however, is a current challenge. Here we present STENCIL-NET, an artificial neural network ","authors_text":"Bevan L. Cheeseman, Christian L. M\\\"uller, Dominik Sturm, Ivo F. Sbalzarini, Suryanarayana Maddu","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2021-01-15T15:43:41Z","title":"STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.06182","kind":"arxiv","version":2},"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":"sha256:365afb6ff2fe70af6a0fb1eee984449c9930cae0f6d371253127b1f03abbd740","target":"record","created_at":"2026-07-05T02:07:34Z","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":"3e00bf11883fa427c7a9618a8733510c9eba242644e203a87d3f31a66268e6f4","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2021-01-15T15:43:41Z","title_canon_sha256":"ee7515229dea512f5154fc2e2a93649aa28fcad781548ff843353e92e3d22c55"},"schema_version":"1.0","source":{"id":"2101.06182","kind":"arxiv","version":2}},"canonical_sha256":"0a6bbb1a7736f67998c35c34c7a5032018b57429c267a918ada430d4cdb84315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6bbb1a7736f67998c35c34c7a5032018b57429c267a918ada430d4cdb84315","first_computed_at":"2026-07-05T02:07:34.089736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:07:34.089736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rFeQvOYJ36gXehBjt/JvEL6dJBtgyguHEfh3VG3cG/Eo0taF44cGQKz7S886NFv5fJUeJpOd0KeUBBS8xc/CCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:07:34.090161Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.06182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:365afb6ff2fe70af6a0fb1eee984449c9930cae0f6d371253127b1f03abbd740","sha256:5b35020aeffe73d23722e81451f8a75b30775c7ab93dec3afed7fb93ef06066f"],"state_sha256":"470a1580064d25f79142996a5f5d9a2b3b814852cd1a1e985846c4a0b0d1b31d"}