{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2AJ7C7L2ON67336VQMT4I7Y6L4","short_pith_number":"pith:2AJ7C7L2","canonical_record":{"source":{"id":"2402.19242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-29T15:18:37Z","cross_cats_sorted":["cs.CE","cs.NA","math.NA"],"title_canon_sha256":"f41f113b979441b2f83a562ecd825f30ce4b65a4fc927a30806241837a04054c","abstract_canon_sha256":"19e5bcfdb989fadd33af615119ebadfb4e12c2ad8bb9cc81df924338ed4171fc"},"schema_version":"1.0"},"canonical_sha256":"d013f17d7a737dfdefd58327c47f1e5f375d9dfe318436eddcf706131abf6928","source":{"kind":"arxiv","id":"2402.19242","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.19242","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"2402.19242v2","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.19242","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"2AJ7C7L2ON67","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_16","alias_value":"2AJ7C7L2ON67336V","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_8","alias_value":"2AJ7C7L2","created_at":"2026-07-05T09:28:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2AJ7C7L2ON67336VQMT4I7Y6L4","target":"record","payload":{"canonical_record":{"source":{"id":"2402.19242","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-29T15:18:37Z","cross_cats_sorted":["cs.CE","cs.NA","math.NA"],"title_canon_sha256":"f41f113b979441b2f83a562ecd825f30ce4b65a4fc927a30806241837a04054c","abstract_canon_sha256":"19e5bcfdb989fadd33af615119ebadfb4e12c2ad8bb9cc81df924338ed4171fc"},"schema_version":"1.0"},"canonical_sha256":"d013f17d7a737dfdefd58327c47f1e5f375d9dfe318436eddcf706131abf6928","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:29.573280Z","signature_b64":"7wSX8OOnfzrxE3A5gLmEUprYsrYOTNdDym2iTx86oFQcnvv/TVQpsv8vf5IdD62BURU6cCTPyiIlbTKcFpa7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d013f17d7a737dfdefd58327c47f1e5f375d9dfe318436eddcf706131abf6928","last_reissued_at":"2026-07-05T09:28:29.572820Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:29.572820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.19242","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:28:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JO91M7De/XSamFPLUyxjLJgZLzTFFgqUA2xXtXD7NzDJAIY4jgCTSAPoHUoPs/0dmvxXGnZTqNgyMeWEvf7UAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:56:02.569095Z"},"content_sha256":"a33a61e44f54cb1cb8bbf9b230371647b9f87614fa358f70812044e3a010bb24","schema_version":"1.0","event_id":"sha256:a33a61e44f54cb1cb8bbf9b230371647b9f87614fa358f70812044e3a010bb24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2AJ7C7L2ON67336VQMT4I7Y6L4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivative-enhanced Deep Operator Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Nolan Bridges, Peng Chen, Yuan Qiu","submitted_at":"2024-02-29T15:18:37Z","abstract_excerpt":"The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.19242","kind":"arxiv","version":2},"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/2402.19242/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":"2026-07-05T09:28:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hOEOCRVJX6l5KbB7Cz+zSm4mKBC4gfw+pr7gcWIT504Ux5FhDFjFB4PbTHSrds6o1uSjtGbyH+E1m1Wsq/2+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:56:02.569626Z"},"content_sha256":"dba3baef90c18e1d73205ebaa1a903d4425f3d5d0b2b68f6347d80aacfc5b7ff","schema_version":"1.0","event_id":"sha256:dba3baef90c18e1d73205ebaa1a903d4425f3d5d0b2b68f6347d80aacfc5b7ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/bundle.json","state_url":"https://pith.science/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/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":"2026-08-10T17:56:02Z","links":{"resolver":"https://pith.science/pith/2AJ7C7L2ON67336VQMT4I7Y6L4","bundle":"https://pith.science/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/bundle.json","state":"https://pith.science/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AJ7C7L2ON67336VQMT4I7Y6L4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2AJ7C7L2ON67336VQMT4I7Y6L4","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":"19e5bcfdb989fadd33af615119ebadfb4e12c2ad8bb9cc81df924338ed4171fc","cross_cats_sorted":["cs.CE","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-29T15:18:37Z","title_canon_sha256":"f41f113b979441b2f83a562ecd825f30ce4b65a4fc927a30806241837a04054c"},"schema_version":"1.0","source":{"id":"2402.19242","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.19242","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"2402.19242v2","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.19242","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"2AJ7C7L2ON67","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_16","alias_value":"2AJ7C7L2ON67336V","created_at":"2026-07-05T09:28:29Z"},{"alias_kind":"pith_short_8","alias_value":"2AJ7C7L2","created_at":"2026-07-05T09:28:29Z"}],"graph_snapshots":[{"event_id":"sha256:dba3baef90c18e1d73205ebaa1a903d4425f3d5d0b2b68f6347d80aacfc5b7ff","target":"graph","created_at":"2026-07-05T09:28:29Z","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/2402.19242/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter in","authors_text":"Nolan Bridges, Peng Chen, Yuan Qiu","cross_cats":["cs.CE","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-29T15:18:37Z","title":"Derivative-enhanced Deep Operator Network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.19242","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:a33a61e44f54cb1cb8bbf9b230371647b9f87614fa358f70812044e3a010bb24","target":"record","created_at":"2026-07-05T09:28:29Z","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":"19e5bcfdb989fadd33af615119ebadfb4e12c2ad8bb9cc81df924338ed4171fc","cross_cats_sorted":["cs.CE","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-02-29T15:18:37Z","title_canon_sha256":"f41f113b979441b2f83a562ecd825f30ce4b65a4fc927a30806241837a04054c"},"schema_version":"1.0","source":{"id":"2402.19242","kind":"arxiv","version":2}},"canonical_sha256":"d013f17d7a737dfdefd58327c47f1e5f375d9dfe318436eddcf706131abf6928","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d013f17d7a737dfdefd58327c47f1e5f375d9dfe318436eddcf706131abf6928","first_computed_at":"2026-07-05T09:28:29.572820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:29.572820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7wSX8OOnfzrxE3A5gLmEUprYsrYOTNdDym2iTx86oFQcnvv/TVQpsv8vf5IdD62BURU6cCTPyiIlbTKcFpa7DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:29.573280Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.19242","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a33a61e44f54cb1cb8bbf9b230371647b9f87614fa358f70812044e3a010bb24","sha256:dba3baef90c18e1d73205ebaa1a903d4425f3d5d0b2b68f6347d80aacfc5b7ff"],"state_sha256":"4cb3e74f326b211c4c21603eb213edd7ac3c34594c8971643bdf88da09633d7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3LK8gAqFY4TjKD+aTYDNt5XFiCtMLXgwUE8WxIpj5vvLDqj2/EIesoHU4Fkr+IjPA36vCckPbk3nLYEyCB5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:56:02.573976Z","bundle_sha256":"c799848d9b359edc0b4dba58513004b724cc9093ca4779e13ad8bc42f672028c"}}