{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:KWS7USHBIK3JN3UFH2H3VMFHVY","short_pith_number":"pith:KWS7USHB","schema_version":"1.0","canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","source":{"kind":"arxiv","id":"2106.03591","version":2},"attestation_state":"computed","paper":{"title":"Calibrating multi-dimensional complex ODE from noisy data via deep neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ME"],"primary_cat":"stat.ML","authors_text":"Fangfang Wang, Fan Yang, Kexuan Li, Ruiqi Liu, Zuofeng Shang","submitted_at":"2021-06-07T13:17:16Z","abstract_excerpt":"Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In this work, we propose a two-stage nonparametric approach to address this problem. We first extract the de-noised data and their higher order derivatives using boundary kernel method, and then feed them into a sparsely connected deep neural network with ReLU activation function. Our method is able to recover the ODE system without being subject to the curse "},"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":"2106.03591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-07T13:17:16Z","cross_cats_sorted":["cs.LG","stat.ME"],"title_canon_sha256":"4697f93be90dae1db3aa595dde4960703a58bc2c9719bc6e01e1024dfebaf67c","abstract_canon_sha256":"c7d16872ff0a2136d3ef393ea91bf76cbcabec47657ca6ae0160aeca662ecc2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:51:58.631993Z","signature_b64":"uUkTZp8eGAXGi43iI/UK403vtTSxrlmPwKb24BPQ2EP8KU6nplueZNS3fzH+pxfnPWwYnTP51z3Ygi2Xs1uOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","last_reissued_at":"2026-07-05T06:51:58.631534Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:51:58.631534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calibrating multi-dimensional complex ODE from noisy data via deep neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ME"],"primary_cat":"stat.ML","authors_text":"Fangfang Wang, Fan Yang, Kexuan Li, Ruiqi Liu, Zuofeng Shang","submitted_at":"2021-06-07T13:17:16Z","abstract_excerpt":"Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In this work, we propose a two-stage nonparametric approach to address this problem. We first extract the de-noised data and their higher order derivatives using boundary kernel method, and then feed them into a sparsely connected deep neural network with ReLU activation function. Our method is able to recover the ODE system without being subject to the curse "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03591","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/2106.03591/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":"2106.03591","created_at":"2026-07-05T06:51:58.631593+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.03591v2","created_at":"2026-07-05T06:51:58.631593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03591","created_at":"2026-07-05T06:51:58.631593+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWS7USHBIK3J","created_at":"2026-07-05T06:51:58.631593+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWS7USHBIK3JN3UF","created_at":"2026-07-05T06:51:58.631593+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWS7USHB","created_at":"2026-07-05T06:51:58.631593+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/KWS7USHBIK3JN3UFH2H3VMFHVY","json":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY.json","graph_json":"https://pith.science/api/pith-number/KWS7USHBIK3JN3UFH2H3VMFHVY/graph.json","events_json":"https://pith.science/api/pith-number/KWS7USHBIK3JN3UFH2H3VMFHVY/events.json","paper":"https://pith.science/paper/KWS7USHB"},"agent_actions":{"view_html":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY","download_json":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY.json","view_paper":"https://pith.science/paper/KWS7USHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.03591&json=true","fetch_graph":"https://pith.science/api/pith-number/KWS7USHBIK3JN3UFH2H3VMFHVY/graph.json","fetch_events":"https://pith.science/api/pith-number/KWS7USHBIK3JN3UFH2H3VMFHVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/action/storage_attestation","attest_author":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/action/author_attestation","sign_citation":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/action/citation_signature","submit_replication":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/action/replication_record"}},"created_at":"2026-07-05T06:51:58.631593+00:00","updated_at":"2026-07-05T06:51:58.631593+00:00"}