{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KWS7USHBIK3JN3UFH2H3VMFHVY","short_pith_number":"pith:KWS7USHB","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"},"canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","source":{"kind":"arxiv","id":"2106.03591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.03591","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"2106.03591v2","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03591","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"KWS7USHBIK3J","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_16","alias_value":"KWS7USHBIK3JN3UF","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_8","alias_value":"KWS7USHB","created_at":"2026-07-05T06:51:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KWS7USHBIK3JN3UFH2H3VMFHVY","target":"record","payload":{"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"},"canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","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"},"source_kind":"arxiv","source_id":"2106.03591","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHDxd65tx06njgeqPXFf0WJKxdNoPjS8BZcg8ah1WQXE9MI/qa5NOcTrf8EEZNwNPp/XvLBhOK/fwYTYl+8cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:48:40.368199Z"},"content_sha256":"d6699a0a2922d70aa2ef92d130bc41d5d243972af1565412160a9b13a855bd2c","schema_version":"1.0","event_id":"sha256:d6699a0a2922d70aa2ef92d130bc41d5d243972af1565412160a9b13a855bd2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KWS7USHBIK3JN3UFH2H3VMFHVY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEPAfgshYuoX28Uiylq0Hp5esbsJ+pL9wBG1IcRhB/Y0LZOEy3sucExEgGZuPPOixXZuUbVsNxmEmkOXX9+YCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:48:40.368725Z"},"content_sha256":"35866ca1d32ce90048d48f452b4910dc49e124dde026dd0c646964a62fcfd0c2","schema_version":"1.0","event_id":"sha256:35866ca1d32ce90048d48f452b4910dc49e124dde026dd0c646964a62fcfd0c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/bundle.json","state_url":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-03T19:48:40Z","links":{"resolver":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY","bundle":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/bundle.json","state":"https://pith.science/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWS7USHBIK3JN3UFH2H3VMFHVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KWS7USHBIK3JN3UFH2H3VMFHVY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c7d16872ff0a2136d3ef393ea91bf76cbcabec47657ca6ae0160aeca662ecc2f","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-07T13:17:16Z","title_canon_sha256":"4697f93be90dae1db3aa595dde4960703a58bc2c9719bc6e01e1024dfebaf67c"},"schema_version":"1.0","source":{"id":"2106.03591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.03591","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"2106.03591v2","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03591","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"KWS7USHBIK3J","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_16","alias_value":"KWS7USHBIK3JN3UF","created_at":"2026-07-05T06:51:58Z"},{"alias_kind":"pith_short_8","alias_value":"KWS7USHB","created_at":"2026-07-05T06:51:58Z"}],"graph_snapshots":[{"event_id":"sha256:35866ca1d32ce90048d48f452b4910dc49e124dde026dd0c646964a62fcfd0c2","target":"graph","created_at":"2026-07-05T06:51:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.03591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Fangfang Wang, Fan Yang, Kexuan Li, Ruiqi Liu, Zuofeng Shang","cross_cats":["cs.LG","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-07T13:17:16Z","title":"Calibrating multi-dimensional complex ODE from noisy data via deep neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03591","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d6699a0a2922d70aa2ef92d130bc41d5d243972af1565412160a9b13a855bd2c","target":"record","created_at":"2026-07-05T06:51:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c7d16872ff0a2136d3ef393ea91bf76cbcabec47657ca6ae0160aeca662ecc2f","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-06-07T13:17:16Z","title_canon_sha256":"4697f93be90dae1db3aa595dde4960703a58bc2c9719bc6e01e1024dfebaf67c"},"schema_version":"1.0","source":{"id":"2106.03591","kind":"arxiv","version":2}},"canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55a5fa48e142b696ee853e8fbab0a7ae00fca7e98b4b50f89db31c3c5acfb544","first_computed_at":"2026-07-05T06:51:58.631534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:51:58.631534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUkTZp8eGAXGi43iI/UK403vtTSxrlmPwKb24BPQ2EP8KU6nplueZNS3fzH+pxfnPWwYnTP51z3Ygi2Xs1uOCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:51:58.631993Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.03591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6699a0a2922d70aa2ef92d130bc41d5d243972af1565412160a9b13a855bd2c","sha256:35866ca1d32ce90048d48f452b4910dc49e124dde026dd0c646964a62fcfd0c2"],"state_sha256":"dfe64ffefc36c546744925033b657542aa41bcf9052985da32316875e714dacf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o06VvfJr4Yp57mSvkojS5y6sauf4bFakO4Me6kcVTcoP2GYAdu0+c2yv3tJ0ucrsg2Xm0enlSCRJXNCmHi6XDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T19:48:40.372201Z","bundle_sha256":"4c219924f7da0b5caf4ab050ac7d8a5be140c77d8343fe85c57f97b104736301"}}