{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:M3C77RS3BU76STTYAWB6BSMNJV","short_pith_number":"pith:M3C77RS3","schema_version":"1.0","canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","source":{"kind":"arxiv","id":"2408.11266","version":5},"attestation_state":"computed","paper":{"title":"Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Georgios Is. Detorakis","submitted_at":"2024-08-21T01:34:20Z","abstract_excerpt":"Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this artic"},"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":"2408.11266","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T01:34:20Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7e090a481e1372b162b66504c9f324bd953573cfebde6a9ff59a0907a8cd1186","abstract_canon_sha256":"e581aa218d9dce49190612ff044db5fb771cea6e3b8acd6dcff6951df8d01110"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:45.041374Z","signature_b64":"/fXWf8Wpu7UikSlrRohm69D9QBacFce67mxmmfwcFaE8Wn0gOWB9py3ENxxU3MFZSEzZ4lGwtCPFuEYze724CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c5ffc65b0d3fe94e780583e0c98d4d4bb4d27667bef6f11698d17cb74f4278","last_reissued_at":"2026-06-02T02:04:45.040895Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:45.040895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Georgios Is. Detorakis","submitted_at":"2024-08-21T01:34:20Z","abstract_excerpt":"Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this artic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11266","kind":"arxiv","version":5},"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/2408.11266/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":"2408.11266","created_at":"2026-06-02T02:04:45.040956+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.11266v5","created_at":"2026-06-02T02:04:45.040956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11266","created_at":"2026-06-02T02:04:45.040956+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3C77RS3BU76","created_at":"2026-06-02T02:04:45.040956+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3C77RS3BU76STTY","created_at":"2026-06-02T02:04:45.040956+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3C77RS3","created_at":"2026-06-02T02:04:45.040956+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/M3C77RS3BU76STTYAWB6BSMNJV","json":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV.json","graph_json":"https://pith.science/api/pith-number/M3C77RS3BU76STTYAWB6BSMNJV/graph.json","events_json":"https://pith.science/api/pith-number/M3C77RS3BU76STTYAWB6BSMNJV/events.json","paper":"https://pith.science/paper/M3C77RS3"},"agent_actions":{"view_html":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV","download_json":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV.json","view_paper":"https://pith.science/paper/M3C77RS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.11266&json=true","fetch_graph":"https://pith.science/api/pith-number/M3C77RS3BU76STTYAWB6BSMNJV/graph.json","fetch_events":"https://pith.science/api/pith-number/M3C77RS3BU76STTYAWB6BSMNJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/action/storage_attestation","attest_author":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/action/author_attestation","sign_citation":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/action/citation_signature","submit_replication":"https://pith.science/pith/M3C77RS3BU76STTYAWB6BSMNJV/action/replication_record"}},"created_at":"2026-06-02T02:04:45.040956+00:00","updated_at":"2026-06-02T02:04:45.040956+00:00"}