{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LDHD3OY663CQJV7GGAWSLLS4TP","short_pith_number":"pith:LDHD3OY6","canonical_record":{"source":{"id":"2111.08823","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-15T02:51:42Z","cross_cats_sorted":["cs.AI","physics.comp-ph"],"title_canon_sha256":"15e9093ea982a0ca1bec4f0d3020c66c0a017cea4b0534281e84e734149ae4f4","abstract_canon_sha256":"6502fcba40232f0d08509fb2b0b1fc1b720e16382178e980ebc77ba77e02b50e"},"schema_version":"1.0"},"canonical_sha256":"58ce3dbb1ef6c504d7e6302d25ae5c9be5a9398ee0a1a029d40acbf477006046","source":{"kind":"arxiv","id":"2111.08823","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.08823","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"2111.08823v3","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.08823","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"LDHD3OY663CQ","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_16","alias_value":"LDHD3OY663CQJV7G","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_8","alias_value":"LDHD3OY6","created_at":"2026-07-05T05:17:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LDHD3OY663CQJV7GGAWSLLS4TP","target":"record","payload":{"canonical_record":{"source":{"id":"2111.08823","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-15T02:51:42Z","cross_cats_sorted":["cs.AI","physics.comp-ph"],"title_canon_sha256":"15e9093ea982a0ca1bec4f0d3020c66c0a017cea4b0534281e84e734149ae4f4","abstract_canon_sha256":"6502fcba40232f0d08509fb2b0b1fc1b720e16382178e980ebc77ba77e02b50e"},"schema_version":"1.0"},"canonical_sha256":"58ce3dbb1ef6c504d7e6302d25ae5c9be5a9398ee0a1a029d40acbf477006046","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:24.166595Z","signature_b64":"fs3yP9uFbKarjnOEPVuOjzjArCg9UrYMva7rwUZGQ/yR5uomebHAvGaxXYsk/K/AETDr4xehL7ikWYOyW1a/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58ce3dbb1ef6c504d7e6302d25ae5c9be5a9398ee0a1a029d40acbf477006046","last_reissued_at":"2026-07-05T05:17:24.166130Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:24.166130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.08823","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jm9zY4J5SYkwYk8DXE5LF9UpO0h+yYh9Aoc/B/Pm++sgey7LeM1nZIL0xA8MA4R8fd/1/gFpXHo0ZFuE4ybJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:05:45.243522Z"},"content_sha256":"7dec4db56b0f4bfd42a89393f2af2a5b47b717bc1936e03c77919e96507e3028","schema_version":"1.0","event_id":"sha256:7dec4db56b0f4bfd42a89393f2af2a5b47b717bc1936e03c77919e96507e3028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LDHD3OY663CQJV7GGAWSLLS4TP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Bei Hua, Beiji Shi, Bin Dong, Bingya Weng, Fan Yu, Haotian Chu, Hongsheng Liu, Kang Yang, Lei Chen, Min Wang, Xiang Huang, Yang Li, Zhanhong Ye, Zidong Wang","submitted_at":"2021-11-15T02:51:42Z","abstract_excerpt":"Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc. Recently, building learning-based numerical solvers for parametric PDEs has become an emerging new field. One category of methods such as the Deep Galerkin Method (DGM) and Physics-Informed Neural Networks (PINNs) aim to approximate the solution of the PDEs. They are typically unsupervised and mesh-free, but require going through the time-consuming network traini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08823","kind":"arxiv","version":3},"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/2111.08823/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":"2026-07-05T05:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzooWzq2lEHkWkblx/6HoKLAbguf/stR9dI18BGcMdGCEqHX3lmZrrDXhTgmAkRaCiZRiOrpmI/uXypTpkdqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:05:45.244585Z"},"content_sha256":"e637e42fa822320255a89f6cb665a8d488b055da160d9abd77663cdf8135e852","schema_version":"1.0","event_id":"sha256:e637e42fa822320255a89f6cb665a8d488b055da160d9abd77663cdf8135e852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDHD3OY663CQJV7GGAWSLLS4TP/bundle.json","state_url":"https://pith.science/pith/LDHD3OY663CQJV7GGAWSLLS4TP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDHD3OY663CQJV7GGAWSLLS4TP/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":"2026-08-19T05:05:45Z","links":{"resolver":"https://pith.science/pith/LDHD3OY663CQJV7GGAWSLLS4TP","bundle":"https://pith.science/pith/LDHD3OY663CQJV7GGAWSLLS4TP/bundle.json","state":"https://pith.science/pith/LDHD3OY663CQJV7GGAWSLLS4TP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDHD3OY663CQJV7GGAWSLLS4TP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LDHD3OY663CQJV7GGAWSLLS4TP","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":"6502fcba40232f0d08509fb2b0b1fc1b720e16382178e980ebc77ba77e02b50e","cross_cats_sorted":["cs.AI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-15T02:51:42Z","title_canon_sha256":"15e9093ea982a0ca1bec4f0d3020c66c0a017cea4b0534281e84e734149ae4f4"},"schema_version":"1.0","source":{"id":"2111.08823","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.08823","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"2111.08823v3","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.08823","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"LDHD3OY663CQ","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_16","alias_value":"LDHD3OY663CQJV7G","created_at":"2026-07-05T05:17:24Z"},{"alias_kind":"pith_short_8","alias_value":"LDHD3OY6","created_at":"2026-07-05T05:17:24Z"}],"graph_snapshots":[{"event_id":"sha256:e637e42fa822320255a89f6cb665a8d488b055da160d9abd77663cdf8135e852","target":"graph","created_at":"2026-07-05T05:17:24Z","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/2111.08823/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc. Recently, building learning-based numerical solvers for parametric PDEs has become an emerging new field. One category of methods such as the Deep Galerkin Method (DGM) and Physics-Informed Neural Networks (PINNs) aim to approximate the solution of the PDEs. They are typically unsupervised and mesh-free, but require going through the time-consuming network traini","authors_text":"Bei Hua, Beiji Shi, Bin Dong, Bingya Weng, Fan Yu, Haotian Chu, Hongsheng Liu, Kang Yang, Lei Chen, Min Wang, Xiang Huang, Yang Li, Zhanhong Ye, Zidong Wang","cross_cats":["cs.AI","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-15T02:51:42Z","title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08823","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":"sha256:7dec4db56b0f4bfd42a89393f2af2a5b47b717bc1936e03c77919e96507e3028","target":"record","created_at":"2026-07-05T05:17:24Z","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":"6502fcba40232f0d08509fb2b0b1fc1b720e16382178e980ebc77ba77e02b50e","cross_cats_sorted":["cs.AI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-15T02:51:42Z","title_canon_sha256":"15e9093ea982a0ca1bec4f0d3020c66c0a017cea4b0534281e84e734149ae4f4"},"schema_version":"1.0","source":{"id":"2111.08823","kind":"arxiv","version":3}},"canonical_sha256":"58ce3dbb1ef6c504d7e6302d25ae5c9be5a9398ee0a1a029d40acbf477006046","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58ce3dbb1ef6c504d7e6302d25ae5c9be5a9398ee0a1a029d40acbf477006046","first_computed_at":"2026-07-05T05:17:24.166130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:17:24.166130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fs3yP9uFbKarjnOEPVuOjzjArCg9UrYMva7rwUZGQ/yR5uomebHAvGaxXYsk/K/AETDr4xehL7ikWYOyW1a/Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:17:24.166595Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.08823","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dec4db56b0f4bfd42a89393f2af2a5b47b717bc1936e03c77919e96507e3028","sha256:e637e42fa822320255a89f6cb665a8d488b055da160d9abd77663cdf8135e852"],"state_sha256":"0c0010d0ad16974a550c00ad6022f04fd28343e76cc805478ae0bad9106fb714"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dM6FeuOqkjDOOWZvO1NDETUCOMmKFhVBWqxtiPuRlE3hghX0VpyaZVocHfXaM173rBv60eMtI2gRRrIGX0BNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T05:05:45.249978Z","bundle_sha256":"405a2c66d02d1989b8aefe4fdec080cddfeafe048beaa5dca9e6cd2be7654dcc"}}