{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:UDUGISQYLM3WXB54PNV6FUSYTC","short_pith_number":"pith:UDUGISQY","canonical_record":{"source":{"id":"2210.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-09T20:06:08Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"6e2944c13d8b066e91668d1afb2f5d6f6f63ec06f96238f9769ea06c2cfc4794","abstract_canon_sha256":"276bf17636fe3bf76fe278691ef5e586fcc8ee87012cb744973c5712c31279c7"},"schema_version":"1.0"},"canonical_sha256":"a0e8644a185b376b87bc7b6be2d2589888eaf32041f43456fd7b70d965db7b38","source":{"kind":"arxiv","id":"2210.04338","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.04338","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2210.04338v1","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.04338","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"UDUGISQYLM3W","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"UDUGISQYLM3WXB54","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"UDUGISQY","created_at":"2026-07-05T06:25:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:UDUGISQYLM3WXB54PNV6FUSYTC","target":"record","payload":{"canonical_record":{"source":{"id":"2210.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-09T20:06:08Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"6e2944c13d8b066e91668d1afb2f5d6f6f63ec06f96238f9769ea06c2cfc4794","abstract_canon_sha256":"276bf17636fe3bf76fe278691ef5e586fcc8ee87012cb744973c5712c31279c7"},"schema_version":"1.0"},"canonical_sha256":"a0e8644a185b376b87bc7b6be2d2589888eaf32041f43456fd7b70d965db7b38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:25:13.963789Z","signature_b64":"e4S6PhuGm0VG37oQInO1WRNJuQTfwEMpC88VC4sGUaKlygL9K/6nF9+saiih0dd17M+uPDfKnP099YQmTkaIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0e8644a185b376b87bc7b6be2d2589888eaf32041f43456fd7b70d965db7b38","last_reissued_at":"2026-07-05T06:25:13.963394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:25:13.963394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.04338","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":"2026-07-05T06:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWiOrmYKcrJIgWgGyk411ngZa+wuBKxp6uvKEWe2ECBOwdLTETkWF9/0Iu+WZzUAENualZGn+bWC5lcPXg5tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:13:54.981643Z"},"content_sha256":"2ac85f8f560cb6b003c34a2d159cf964353d98839953f5337b92e60e020b10ef","schema_version":"1.0","event_id":"sha256:2ac85f8f560cb6b003c34a2d159cf964353d98839953f5337b92e60e020b10ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:UDUGISQYLM3WXB54PNV6FUSYTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Suchuan Dong, Yiran Wang","submitted_at":"2022-10-09T20:06:08Z","abstract_excerpt":"We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs to inverse problems. We develop three algorithms for training the neural network to solve the inverse PDE problem. The first algorithm (NLLSQ) determines the inverse parameters and the trainable network parameters all together by the nonlinear least squares method with perturbations (NLLSQ-perturb). The second algorithm (VarPro-F1) eliminates the inverse par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04338","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/2210.04338/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":"2026-07-05T06:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNxu5wTBOc2QbNEvF4bH3lQdItZtGMY3eUQtHk2aJ021TuzN4IAGMfHX8Kiz+aIFMZLQwH32Kw3UqzbSxLOYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:13:54.982145Z"},"content_sha256":"58f5ef417d88ee5d25dfbd9d4364ba21aa0bd3c6fb7fca7be317f7be0826a47d","schema_version":"1.0","event_id":"sha256:58f5ef417d88ee5d25dfbd9d4364ba21aa0bd3c6fb7fca7be317f7be0826a47d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDUGISQYLM3WXB54PNV6FUSYTC/bundle.json","state_url":"https://pith.science/pith/UDUGISQYLM3WXB54PNV6FUSYTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDUGISQYLM3WXB54PNV6FUSYTC/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":"2026-08-05T09:13:54Z","links":{"resolver":"https://pith.science/pith/UDUGISQYLM3WXB54PNV6FUSYTC","bundle":"https://pith.science/pith/UDUGISQYLM3WXB54PNV6FUSYTC/bundle.json","state":"https://pith.science/pith/UDUGISQYLM3WXB54PNV6FUSYTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDUGISQYLM3WXB54PNV6FUSYTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UDUGISQYLM3WXB54PNV6FUSYTC","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":"276bf17636fe3bf76fe278691ef5e586fcc8ee87012cb744973c5712c31279c7","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-09T20:06:08Z","title_canon_sha256":"6e2944c13d8b066e91668d1afb2f5d6f6f63ec06f96238f9769ea06c2cfc4794"},"schema_version":"1.0","source":{"id":"2210.04338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.04338","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2210.04338v1","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.04338","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"UDUGISQYLM3W","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"UDUGISQYLM3WXB54","created_at":"2026-07-05T06:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"UDUGISQY","created_at":"2026-07-05T06:25:13Z"}],"graph_snapshots":[{"event_id":"sha256:58f5ef417d88ee5d25dfbd9d4364ba21aa0bd3c6fb7fca7be317f7be0826a47d","target":"graph","created_at":"2026-07-05T06:25:13Z","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/2210.04338/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs to inverse problems. We develop three algorithms for training the neural network to solve the inverse PDE problem. The first algorithm (NLLSQ) determines the inverse parameters and the trainable network parameters all together by the nonlinear least squares method with perturbations (NLLSQ-perturb). The second algorithm (VarPro-F1) eliminates the inverse par","authors_text":"Suchuan Dong, Yiran Wang","cross_cats":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-09T20:06:08Z","title":"A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04338","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":"sha256:2ac85f8f560cb6b003c34a2d159cf964353d98839953f5337b92e60e020b10ef","target":"record","created_at":"2026-07-05T06:25:13Z","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":"276bf17636fe3bf76fe278691ef5e586fcc8ee87012cb744973c5712c31279c7","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-10-09T20:06:08Z","title_canon_sha256":"6e2944c13d8b066e91668d1afb2f5d6f6f63ec06f96238f9769ea06c2cfc4794"},"schema_version":"1.0","source":{"id":"2210.04338","kind":"arxiv","version":1}},"canonical_sha256":"a0e8644a185b376b87bc7b6be2d2589888eaf32041f43456fd7b70d965db7b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0e8644a185b376b87bc7b6be2d2589888eaf32041f43456fd7b70d965db7b38","first_computed_at":"2026-07-05T06:25:13.963394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:25:13.963394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4S6PhuGm0VG37oQInO1WRNJuQTfwEMpC88VC4sGUaKlygL9K/6nF9+saiih0dd17M+uPDfKnP099YQmTkaIDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:25:13.963789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.04338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ac85f8f560cb6b003c34a2d159cf964353d98839953f5337b92e60e020b10ef","sha256:58f5ef417d88ee5d25dfbd9d4364ba21aa0bd3c6fb7fca7be317f7be0826a47d"],"state_sha256":"0b99021e1dc9a59fd27dfb0f009d52127c9095676c15f7933b91e0e9e17c19e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZeShHF+vevFi+yqlAMWU1AbUrQxtylbitV/v5saIA9c7Rd2Z0qwvnUCYbicv3AzkrRtWPujCI3pCazjHdv+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T09:13:54.987074Z","bundle_sha256":"5897e57bc3b42db6558588d3cd9268fa85a43abab942663d25dc70128154a890"}}