{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QT45IHGZQVTY4NWJYD3M5YOCSA","short_pith_number":"pith:QT45IHGZ","schema_version":"1.0","canonical_sha256":"84f9d41cd985678e36c9c0f6cee1c290082c210841a1642fe5e7d5a5ed1cea9d","source":{"kind":"arxiv","id":"2409.14248","version":3},"attestation_state":"computed","paper":{"title":"Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.CE","cs.LG","physics.comp-ph"],"primary_cat":"cs.NE","authors_text":"Chi Chiu SO, Siu Pang Yung","submitted_at":"2024-08-09T03:50:58Z","abstract_excerpt":"Finding solutions to partial differential equations (PDEs) is an important and essential component in many scientific and engineering discoveries. One of the common approaches empowered by deep learning is Physics-informed Neural Networks (PINNs). Recently, a new type of fundamental neural network model, Kolmogorov-Arnold Networks (KANs), has been proposed as a substitute of Multilayer Perceptions (MLPs), and possesses trainable activation functions. To enhance KANs in fitting accuracy, a modification of KANs, so called ReLU-KANs, using \"square of ReLU\" as the basis of its activation functions"},"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":"2409.14248","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-08-09T03:50:58Z","cross_cats_sorted":["cs.AI","cs.CE","cs.LG","physics.comp-ph"],"title_canon_sha256":"7c41bc93a44b7ab441aa83eb3f5e13ebb3e6ea7ff0c1c82f4d2045c2f38a951e","abstract_canon_sha256":"55bc7e1078cfe100a6dc6fe15ffbc23398444b5e34435d874457bda8a611affd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:13:07.832093Z","signature_b64":"YWyl4jlR4Jbz2DI4yi8kDNjilfHK3A4+cQOg2ygdSvJdi7yTq091w3xEuZ9ypsAFqc6yPbVSbMXwaUeObLNTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84f9d41cd985678e36c9c0f6cee1c290082c210841a1642fe5e7d5a5ed1cea9d","last_reissued_at":"2026-07-05T09:13:07.831520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:13:07.831520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.CE","cs.LG","physics.comp-ph"],"primary_cat":"cs.NE","authors_text":"Chi Chiu SO, Siu Pang Yung","submitted_at":"2024-08-09T03:50:58Z","abstract_excerpt":"Finding solutions to partial differential equations (PDEs) is an important and essential component in many scientific and engineering discoveries. One of the common approaches empowered by deep learning is Physics-informed Neural Networks (PINNs). Recently, a new type of fundamental neural network model, Kolmogorov-Arnold Networks (KANs), has been proposed as a substitute of Multilayer Perceptions (MLPs), and possesses trainable activation functions. To enhance KANs in fitting accuracy, a modification of KANs, so called ReLU-KANs, using \"square of ReLU\" as the basis of its activation functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14248","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/2409.14248/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":"2409.14248","created_at":"2026-07-05T09:13:07.831579+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.14248v3","created_at":"2026-07-05T09:13:07.831579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14248","created_at":"2026-07-05T09:13:07.831579+00:00"},{"alias_kind":"pith_short_12","alias_value":"QT45IHGZQVTY","created_at":"2026-07-05T09:13:07.831579+00:00"},{"alias_kind":"pith_short_16","alias_value":"QT45IHGZQVTY4NWJ","created_at":"2026-07-05T09:13:07.831579+00:00"},{"alias_kind":"pith_short_8","alias_value":"QT45IHGZ","created_at":"2026-07-05T09:13:07.831579+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.29688","citing_title":"A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2410.03801","citing_title":"P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2605.19536","citing_title":"A Dual Physics-Informed Kolmogorov-Arnold Neural Network Framework for Continuum Topology Optimization","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2510.25781","citing_title":"A Practitioner's Guide to Kolmogorov-Arnold Networks","ref_index":140,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23599","citing_title":"Partition-of-Unity Gaussian Kolmogorov-Arnold Networks","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21174","citing_title":"Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA","json":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA.json","graph_json":"https://pith.science/api/pith-number/QT45IHGZQVTY4NWJYD3M5YOCSA/graph.json","events_json":"https://pith.science/api/pith-number/QT45IHGZQVTY4NWJYD3M5YOCSA/events.json","paper":"https://pith.science/paper/QT45IHGZ"},"agent_actions":{"view_html":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA","download_json":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA.json","view_paper":"https://pith.science/paper/QT45IHGZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.14248&json=true","fetch_graph":"https://pith.science/api/pith-number/QT45IHGZQVTY4NWJYD3M5YOCSA/graph.json","fetch_events":"https://pith.science/api/pith-number/QT45IHGZQVTY4NWJYD3M5YOCSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA/action/storage_attestation","attest_author":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA/action/author_attestation","sign_citation":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA/action/citation_signature","submit_replication":"https://pith.science/pith/QT45IHGZQVTY4NWJYD3M5YOCSA/action/replication_record"}},"created_at":"2026-07-05T09:13:07.831579+00:00","updated_at":"2026-07-05T09:13:07.831579+00:00"}