{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZRY7BORLUVZRFYHEV2RCBW3TOD","short_pith_number":"pith:ZRY7BORL","schema_version":"1.0","canonical_sha256":"cc71f0ba2ba57312e0e4aea220db7370fbca48a71adb9bc54be5849dcc4e8d05","source":{"kind":"arxiv","id":"2505.11682","version":1},"attestation_state":"computed","paper":{"title":"Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ananyae Kumar Bhartari, Vinayak Vinayak, Vivek B Shenoy","submitted_at":"2025-05-16T20:43:53Z","abstract_excerpt":"Parameter estimation in inverse problems involving partial differential equations (PDEs) underpins modeling across scientific disciplines, especially when parameters vary in space or time. Physics-informed Machine Learning (PhiML) integrates PDE constraints into deep learning, but prevailing approaches depend on recursive automatic differentiation (autodiff), which produces inaccurate high-order derivatives, inflates memory usage, and underperforms in noisy settings. We propose Mollifier Layers, a lightweight, architecture-agnostic module that replaces autodiff with convolutional operations us"},"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":"2505.11682","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-16T20:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"f1a0ab090625e030cbb599741a0018ab501121246fa7a22d2ed1dbe34dae548a","abstract_canon_sha256":"ef55206da31598c93583abdef2e1fcf19cc0a0cd69c0dcfa2dc423beac546d0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:25.410872Z","signature_b64":"ugm+AYq+FQc323yqo+7+1nMiVGHoEPSvALOhLA7ntXZiw0cA098HYqeOYvvwLLyX7VJn/XCxY8363BpuKhTaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc71f0ba2ba57312e0e4aea220db7370fbca48a71adb9bc54be5849dcc4e8d05","last_reissued_at":"2026-07-05T11:04:25.410390Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:25.410390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ananyae Kumar Bhartari, Vinayak Vinayak, Vivek B Shenoy","submitted_at":"2025-05-16T20:43:53Z","abstract_excerpt":"Parameter estimation in inverse problems involving partial differential equations (PDEs) underpins modeling across scientific disciplines, especially when parameters vary in space or time. Physics-informed Machine Learning (PhiML) integrates PDE constraints into deep learning, but prevailing approaches depend on recursive automatic differentiation (autodiff), which produces inaccurate high-order derivatives, inflates memory usage, and underperforms in noisy settings. We propose Mollifier Layers, a lightweight, architecture-agnostic module that replaces autodiff with convolutional operations us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11682","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/2505.11682/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":"2505.11682","created_at":"2026-07-05T11:04:25.410455+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.11682v1","created_at":"2026-07-05T11:04:25.410455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11682","created_at":"2026-07-05T11:04:25.410455+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRY7BORLUVZR","created_at":"2026-07-05T11:04:25.410455+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRY7BORLUVZRFYHE","created_at":"2026-07-05T11:04:25.410455+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRY7BORL","created_at":"2026-07-05T11:04:25.410455+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD","json":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD.json","graph_json":"https://pith.science/api/pith-number/ZRY7BORLUVZRFYHEV2RCBW3TOD/graph.json","events_json":"https://pith.science/api/pith-number/ZRY7BORLUVZRFYHEV2RCBW3TOD/events.json","paper":"https://pith.science/paper/ZRY7BORL"},"agent_actions":{"view_html":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD","download_json":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD.json","view_paper":"https://pith.science/paper/ZRY7BORL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.11682&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRY7BORLUVZRFYHEV2RCBW3TOD/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRY7BORLUVZRFYHEV2RCBW3TOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD/action/storage_attestation","attest_author":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD/action/author_attestation","sign_citation":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD/action/citation_signature","submit_replication":"https://pith.science/pith/ZRY7BORLUVZRFYHEV2RCBW3TOD/action/replication_record"}},"created_at":"2026-07-05T11:04:25.410455+00:00","updated_at":"2026-07-05T11:04:25.410455+00:00"}