{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:EGCAILJI3GBEKHUOAMDLY2OT4R","short_pith_number":"pith:EGCAILJI","schema_version":"1.0","canonical_sha256":"2184042d28d982451e8e0306bc69d3e4533a01419117182530fd906f7828b8c0","source":{"kind":"arxiv","id":"2203.08205","version":1},"attestation_state":"computed","paper":{"title":"Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cs.LG","authors_text":"Chung-Hao Lee, Colton J. Ross, Huaiqian You, Quinn Zhang, Yue Yu","submitted_at":"2022-03-15T19:08:13Z","abstract_excerpt":"Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are present, these classical models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation and/or experimental measurements to predict a material's response without using conventional constitutive models. Specifically, the material response is modeled by learning the implicit mappings betwee"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2203.08205","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-03-15T19:08:13Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"3b6e29b5421318e40afacdb54389dda3c7641002302e3995b57fd6b78c8f4d48","abstract_canon_sha256":"6a09b7e54057875da2ac55162abcaaa87f2ba8940ed0ef3dbaf84686b6952d47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:41.044900Z","signature_b64":"KsrpirYp0BrvKZgr21g5X1UpJo+gDkiwFYOAtX7qtNobJlSinUKMj8LqR3g9f4WDKfqEuEf06Xne7SnGuGrtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2184042d28d982451e8e0306bc69d3e4533a01419117182530fd906f7828b8c0","last_reissued_at":"2026-07-05T04:43:41.044355Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:41.044355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cs.LG","authors_text":"Chung-Hao Lee, Colton J. Ross, Huaiqian You, Quinn Zhang, Yue Yu","submitted_at":"2022-03-15T19:08:13Z","abstract_excerpt":"Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are present, these classical models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation and/or experimental measurements to predict a material's response without using conventional constitutive models. Specifically, the material response is modeled by learning the implicit mappings betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.08205","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/2203.08205/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2203.08205","created_at":"2026-07-05T04:43:41.044429+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.08205v1","created_at":"2026-07-05T04:43:41.044429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.08205","created_at":"2026-07-05T04:43:41.044429+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGCAILJI3GBE","created_at":"2026-07-05T04:43:41.044429+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGCAILJI3GBEKHUO","created_at":"2026-07-05T04:43:41.044429+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGCAILJI","created_at":"2026-07-05T04:43:41.044429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07129","citing_title":"Fourier-enhanced Neural Networks For Systems Biology Applications","ref_index":65,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R","json":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R.json","graph_json":"https://pith.science/api/pith-number/EGCAILJI3GBEKHUOAMDLY2OT4R/graph.json","events_json":"https://pith.science/api/pith-number/EGCAILJI3GBEKHUOAMDLY2OT4R/events.json","paper":"https://pith.science/paper/EGCAILJI"},"agent_actions":{"view_html":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R","download_json":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R.json","view_paper":"https://pith.science/paper/EGCAILJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.08205&json=true","fetch_graph":"https://pith.science/api/pith-number/EGCAILJI3GBEKHUOAMDLY2OT4R/graph.json","fetch_events":"https://pith.science/api/pith-number/EGCAILJI3GBEKHUOAMDLY2OT4R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R/action/storage_attestation","attest_author":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R/action/author_attestation","sign_citation":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R/action/citation_signature","submit_replication":"https://pith.science/pith/EGCAILJI3GBEKHUOAMDLY2OT4R/action/replication_record"}},"created_at":"2026-07-05T04:43:41.044429+00:00","updated_at":"2026-07-05T04:43:41.044429+00:00"}