{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AG3UJZCYZINQINQZ7IIOMVCYS3","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":"ae65aaac6160d916556404eaef36afad5a869365181f2247709f85010346ae54","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-01T16:26:53Z","title_canon_sha256":"6beb5598e817b8df51754c76e700023f11283dc80218808bd125756ac7409ac3"},"schema_version":"1.0","source":{"id":"2502.00488","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00488","created_at":"2026-07-05T11:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00488v3","created_at":"2026-07-05T11:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00488","created_at":"2026-07-05T11:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"AG3UJZCYZINQ","created_at":"2026-07-05T11:11:40Z"},{"alias_kind":"pith_short_16","alias_value":"AG3UJZCYZINQINQZ","created_at":"2026-07-05T11:11:40Z"},{"alias_kind":"pith_short_8","alias_value":"AG3UJZCY","created_at":"2026-07-05T11:11:40Z"}],"graph_snapshots":[{"event_id":"sha256:2b735209efc868d4323c81e55f8a3d15ff3d27e69f2fde1f1bd36e85706baeb2","target":"graph","created_at":"2026-07-05T11:11:40Z","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/2502.00488/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters in the PDEs that introduce near-singularities in the loss function. In this study, we overcome this challenge by introducing a novel method based on homotopy dynamics to effectively manipulate these parameters. From a theoretical perspective, we analyze the effects of these parameters on training difficulty in these singularly perturbed problems and establis","authors_text":"Chuqi Chen, Wenrui Hao, Yahong Yang, Yang Xiang","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-01T16:26:53Z","title":"Learn Singularly Perturbed Solutions via Homotopy Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00488","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":"sha256:1a88d1e283113c348ab4cbeaf3e91945e5309afa21f2d797867dfc121e594bdb","target":"record","created_at":"2026-07-05T11:11:40Z","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":"ae65aaac6160d916556404eaef36afad5a869365181f2247709f85010346ae54","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-01T16:26:53Z","title_canon_sha256":"6beb5598e817b8df51754c76e700023f11283dc80218808bd125756ac7409ac3"},"schema_version":"1.0","source":{"id":"2502.00488","kind":"arxiv","version":3}},"canonical_sha256":"01b744e458ca1b043619fa10e6545896dc2364d942d299891a5639ff65e26574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01b744e458ca1b043619fa10e6545896dc2364d942d299891a5639ff65e26574","first_computed_at":"2026-07-05T11:11:40.351811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:40.351811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BdAj7y7TFIL8a1q1NBXxKZ8ntTYvNvecEm+Hk9OK44xHqB+AMS1tIcM3WioGiuCmSVrZE4FQ796aAIqytC1ADQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:40.352292Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.00488","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a88d1e283113c348ab4cbeaf3e91945e5309afa21f2d797867dfc121e594bdb","sha256:2b735209efc868d4323c81e55f8a3d15ff3d27e69f2fde1f1bd36e85706baeb2"],"state_sha256":"04869d3d629742f316d3ace753758d2d646d8d53b008eb4e5556f4b336b51358"}