{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:U2QLGBZI6OUXOONRWFG4TOV7LC","short_pith_number":"pith:U2QLGBZI","schema_version":"1.0","canonical_sha256":"a6a0b30728f3a97739b1b14dc9babf58aa3e36b198bfcb9ef514cf99bda100da","source":{"kind":"arxiv","id":"2205.02191","version":1},"attestation_state":"computed","paper":{"title":"Wavelet neural operator: a neural operator for parametric partial differential equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"physics.comp-ph","authors_text":"Souvik Chakraborty, Tapas Tripura","submitted_at":"2022-05-04T17:13:59Z","abstract_excerpt":"With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible alternative in this context is to utilize operator learning algorithm that directly learn nonlinear mapping between two functional spaces; this facilitates real-time prediction of naturally arising complex evolutionary dynamics. In this work, we introduce a novel operator learning algorithm referred to as the Wavelet Neural Operator (WNO) that blends integral kernel"},"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":"2205.02191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2022-05-04T17:13:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"128520e2b53126a359c855dcc1a7c89b9a77b3ff6ba75467045e52ae67d2f03d","abstract_canon_sha256":"0989c0c33e7b90b4f21b7e831a031ea26d791aec4a427ec6333e85dd04a5ac5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:25.950852Z","signature_b64":"qaqWlkeNMAYrPvFenwOj8c2Yyq2622Mv3l0iUFerpIDCFyzWWm5WSm5aY7GEXAcMzbNjxQj3YEl2afE0VueMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a0b30728f3a97739b1b14dc9babf58aa3e36b198bfcb9ef514cf99bda100da","last_reissued_at":"2026-07-05T04:20:25.950420Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:25.950420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wavelet neural operator: a neural operator for parametric partial differential equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"physics.comp-ph","authors_text":"Souvik Chakraborty, Tapas Tripura","submitted_at":"2022-05-04T17:13:59Z","abstract_excerpt":"With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible alternative in this context is to utilize operator learning algorithm that directly learn nonlinear mapping between two functional spaces; this facilitates real-time prediction of naturally arising complex evolutionary dynamics. In this work, we introduce a novel operator learning algorithm referred to as the Wavelet Neural Operator (WNO) that blends integral kernel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.02191","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/2205.02191/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":"2205.02191","created_at":"2026-07-05T04:20:25.950477+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.02191v1","created_at":"2026-07-05T04:20:25.950477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.02191","created_at":"2026-07-05T04:20:25.950477+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2QLGBZI6OUX","created_at":"2026-07-05T04:20:25.950477+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2QLGBZI6OUXOONR","created_at":"2026-07-05T04:20:25.950477+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2QLGBZI","created_at":"2026-07-05T04:20:25.950477+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":14,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25820","citing_title":"Operator Learning on the Data-Driven Multiscale Space for Nonlinear Flow in Random Heterogeneous Porous Media","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2607.01128","citing_title":"GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2606.02427","citing_title":"Spectral Audit of In-Context Operator Networks","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.25115","citing_title":"Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.25949","citing_title":"Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31559","citing_title":"Functional Attention: From Pairwise Affinities to Functional Correspondences","ref_index":12,"is_internal_anchor":false},{"citing_arxiv_id":"2510.00233","citing_title":"Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08935","citing_title":"PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting","ref_index":164,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12965","citing_title":"U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08935","citing_title":"PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting","ref_index":164,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10451","citing_title":"Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08915","citing_title":"Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow","ref_index":72,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19027","citing_title":"Neural Operator Representation of Granular Micromechanics-based Failure Envelope","ref_index":87,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08076","citing_title":"$\\phi-$DeepONet: A Discontinuity Capturing Neural Operator","ref_index":23,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC","json":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC.json","graph_json":"https://pith.science/api/pith-number/U2QLGBZI6OUXOONRWFG4TOV7LC/graph.json","events_json":"https://pith.science/api/pith-number/U2QLGBZI6OUXOONRWFG4TOV7LC/events.json","paper":"https://pith.science/paper/U2QLGBZI"},"agent_actions":{"view_html":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC","download_json":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC.json","view_paper":"https://pith.science/paper/U2QLGBZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.02191&json=true","fetch_graph":"https://pith.science/api/pith-number/U2QLGBZI6OUXOONRWFG4TOV7LC/graph.json","fetch_events":"https://pith.science/api/pith-number/U2QLGBZI6OUXOONRWFG4TOV7LC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC/action/storage_attestation","attest_author":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC/action/author_attestation","sign_citation":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC/action/citation_signature","submit_replication":"https://pith.science/pith/U2QLGBZI6OUXOONRWFG4TOV7LC/action/replication_record"}},"created_at":"2026-07-05T04:20:25.950477+00:00","updated_at":"2026-07-05T04:20:25.950477+00:00"}