{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SWPGN3CZRAOVL2QRKOJ3XCNH2T","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":"685ec668cb336cc44fac1661d1ca3ace088a4fd320f5113681f2c5ce19ef6b19","cross_cats_sorted":["cs.AI","hep-th","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-21T13:25:56Z","title_canon_sha256":"e13853b070b29f1e16b390426cc05534aeec1876ac5ec6abfa8f3b45fb8065d3"},"schema_version":"1.0","source":{"id":"2501.12116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.12116","created_at":"2026-07-05T11:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"2501.12116v2","created_at":"2026-07-05T11:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.12116","created_at":"2026-07-05T11:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"SWPGN3CZRAOV","created_at":"2026-07-05T11:59:56Z"},{"alias_kind":"pith_short_16","alias_value":"SWPGN3CZRAOVL2QR","created_at":"2026-07-05T11:59:56Z"},{"alias_kind":"pith_short_8","alias_value":"SWPGN3CZ","created_at":"2026-07-05T11:59:56Z"}],"graph_snapshots":[{"event_id":"sha256:863d454e9ce07ec8c7450a807f07ce77992c0c125eca77815b81c08d302a95c7","target":"graph","created_at":"2026-07-05T11:59:56Z","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/2501.12116/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to facilitate the solution of nonlinear multiscale differential equations and, especially, inverse problems using Physics-Informed Neural Networks (PINNs). This framework is based on what is called \\textit{multi-head} (MH) training, which involves training the network to learn a general space of all solutions for a given set of equations with certain variability, ","authors_text":"Pablo Tejerina-P\\'erez, Pavlos Protopapas, Pedro Taranc\\'on-\\'Alvarez, Raul Jimenez","cross_cats":["cs.AI","hep-th","math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-21T13:25:56Z","title":"Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12116","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":"sha256:9abce5fb09e47208e9b565fd229b275fb4293c1b4381e032ee9339f921be1034","target":"record","created_at":"2026-07-05T11:59:56Z","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":"685ec668cb336cc44fac1661d1ca3ace088a4fd320f5113681f2c5ce19ef6b19","cross_cats_sorted":["cs.AI","hep-th","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-21T13:25:56Z","title_canon_sha256":"e13853b070b29f1e16b390426cc05534aeec1876ac5ec6abfa8f3b45fb8065d3"},"schema_version":"1.0","source":{"id":"2501.12116","kind":"arxiv","version":2}},"canonical_sha256":"959e66ec59881d55ea115393bb89a7d4d418a7c0238b5427a1622e02dbccebaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"959e66ec59881d55ea115393bb89a7d4d418a7c0238b5427a1622e02dbccebaa","first_computed_at":"2026-07-05T11:59:56.845434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:56.845434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uaucrdNM6EfToJn4mvSdO2W5H0OaaTo2z90qQ6RY8c9oz4XMOyaVRX/80+97ErB4Y8Te8FkTD688L83WpY9AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:56.845865Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.12116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9abce5fb09e47208e9b565fd229b275fb4293c1b4381e032ee9339f921be1034","sha256:863d454e9ce07ec8c7450a807f07ce77992c0c125eca77815b81c08d302a95c7"],"state_sha256":"bc0fda437fd72cbaf7f7985e11ec8e9db222b1da37de6db856c85e45075abab7"}