{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ZV4VKF6WDADTM44BMK5SXUOBV2","short_pith_number":"pith:ZV4VKF6W","canonical_record":{"source":{"id":"2303.01767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-03T08:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"e3478884b084ddbe10febedede9bca849dd9c0293aef154ca658d799d9986417","abstract_canon_sha256":"6a697066c6b281b075dc733e1c479994d6fa7d11ebec39aa2dd750245d0df1f2"},"schema_version":"1.0"},"canonical_sha256":"cd795517d6180736738162bb2bd1c1aebd3f3cec956c7bee549f9e4aa1fea26e","source":{"kind":"arxiv","id":"2303.01767","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01767","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01767v1","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01767","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZV4VKF6WDADT","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"ZV4VKF6WDADTM44B","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"ZV4VKF6W","created_at":"2026-07-05T05:47:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ZV4VKF6WDADTM44BMK5SXUOBV2","target":"record","payload":{"canonical_record":{"source":{"id":"2303.01767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-03T08:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"e3478884b084ddbe10febedede9bca849dd9c0293aef154ca658d799d9986417","abstract_canon_sha256":"6a697066c6b281b075dc733e1c479994d6fa7d11ebec39aa2dd750245d0df1f2"},"schema_version":"1.0"},"canonical_sha256":"cd795517d6180736738162bb2bd1c1aebd3f3cec956c7bee549f9e4aa1fea26e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:48.614026Z","signature_b64":"jCZCscLaZg0GDy5PWSeJFvhZ+4aObPAsnxLK/y7mqD1WK+xkb9Ley1FGaYpEHr8C6wwqQAyIBjaXWSfN7bs6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd795517d6180736738162bb2bd1c1aebd3f3cec956c7bee549f9e4aa1fea26e","last_reissued_at":"2026-07-05T05:47:48.613425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:48.613425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.01767","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LLOobyQLx0gnZQ7RY8pZNlFRAInljcrvTSbWti3kJ7uRRmc1ZmCfe4ddF9I/WJh9Gcum694Kmt9O5RWKE6fDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:14:03.604961Z"},"content_sha256":"20ff5389f545eb997d8cb9c24a19bdd52363e0a9c25eb0ebcbd2e01ad7108461","schema_version":"1.0","event_id":"sha256:20ff5389f545eb997d8cb9c24a19bdd52363e0a9c25eb0ebcbd2e01ad7108461"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ZV4VKF6WDADTM44BMK5SXUOBV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Sheng-Jun Huang, Song-Can Chen, Ye Li","submitted_at":"2023-03-03T08:17:47Z","abstract_excerpt":"Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process. We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions. We theoretically prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01767","kind":"arxiv","version":1},"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/2303.01767/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":"2026-07-05T05:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9lU1VNhk6ZVQaDsIpzXRehYGq3FSC+v/P9qzEPUcD9+RPqG+NYMVtxgF85v6w7KPBZEslpu6ElZjFVaq9kbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:14:03.605480Z"},"content_sha256":"b8b4acde029a49f1a9587474545f0393d2288eee61dc84676e96228e61f70cc7","schema_version":"1.0","event_id":"sha256:b8b4acde029a49f1a9587474545f0393d2288eee61dc84676e96228e61f70cc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/bundle.json","state_url":"https://pith.science/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/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":"2026-08-21T01:14:03Z","links":{"resolver":"https://pith.science/pith/ZV4VKF6WDADTM44BMK5SXUOBV2","bundle":"https://pith.science/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/bundle.json","state":"https://pith.science/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZV4VKF6WDADTM44BMK5SXUOBV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZV4VKF6WDADTM44BMK5SXUOBV2","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":"6a697066c6b281b075dc733e1c479994d6fa7d11ebec39aa2dd750245d0df1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-03T08:17:47Z","title_canon_sha256":"e3478884b084ddbe10febedede9bca849dd9c0293aef154ca658d799d9986417"},"schema_version":"1.0","source":{"id":"2303.01767","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01767","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01767v1","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01767","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZV4VKF6WDADT","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"ZV4VKF6WDADTM44B","created_at":"2026-07-05T05:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"ZV4VKF6W","created_at":"2026-07-05T05:47:48Z"}],"graph_snapshots":[{"event_id":"sha256:b8b4acde029a49f1a9587474545f0393d2288eee61dc84676e96228e61f70cc7","target":"graph","created_at":"2026-07-05T05:47:48Z","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/2303.01767/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process. We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions. We theoretically prove t","authors_text":"Sheng-Jun Huang, Song-Can Chen, Ye Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-03T08:17:47Z","title":"Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01767","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":"sha256:20ff5389f545eb997d8cb9c24a19bdd52363e0a9c25eb0ebcbd2e01ad7108461","target":"record","created_at":"2026-07-05T05:47:48Z","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":"6a697066c6b281b075dc733e1c479994d6fa7d11ebec39aa2dd750245d0df1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-03T08:17:47Z","title_canon_sha256":"e3478884b084ddbe10febedede9bca849dd9c0293aef154ca658d799d9986417"},"schema_version":"1.0","source":{"id":"2303.01767","kind":"arxiv","version":1}},"canonical_sha256":"cd795517d6180736738162bb2bd1c1aebd3f3cec956c7bee549f9e4aa1fea26e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd795517d6180736738162bb2bd1c1aebd3f3cec956c7bee549f9e4aa1fea26e","first_computed_at":"2026-07-05T05:47:48.613425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:48.613425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jCZCscLaZg0GDy5PWSeJFvhZ+4aObPAsnxLK/y7mqD1WK+xkb9Ley1FGaYpEHr8C6wwqQAyIBjaXWSfN7bs6AA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:48.614026Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.01767","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ff5389f545eb997d8cb9c24a19bdd52363e0a9c25eb0ebcbd2e01ad7108461","sha256:b8b4acde029a49f1a9587474545f0393d2288eee61dc84676e96228e61f70cc7"],"state_sha256":"f290c4af47f1a174cf31bad8e02d7cc4fa7a4a45547f1f592592418cda5ceed3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8HltqsBDbu1B71yRPxJUVFMKBgEbp6qXAfaHjQi2ZfAbjyCxuzqXBMHASBHOunIuTNVjWjsGS5w13N/JcmnCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:14:03.610895Z","bundle_sha256":"d37f142e9cdbfa660cf4a271b55d456544594ac535928cec6987dd6ce97974ea"}}