{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4QH5KWJIOTMN6JORR7I3FA3BV3","short_pith_number":"pith:4QH5KWJI","schema_version":"1.0","canonical_sha256":"e40fd5592874d8df25d18fd1b28361aef3100c3960bdebf1e05b60e3afea0682","source":{"kind":"arxiv","id":"1811.08782","version":1},"attestation_state":"computed","paper":{"title":"Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.CP","authors_text":"Adolfo Correia, Ali Al-Aradi, Danilo Naiff, Gabriel Jardim, Yuri Saporito","submitted_at":"2018-11-21T15:34:05Z","abstract_excerpt":"In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal execution, mean field games, etc. The main idea behind DGM is to represent the unknown function of interest using a deep neural network. A key feature of this approach is the fact that, unlike other commonly used numerical approaches such as finite difference methods, it is mesh-free. As such, it does not suffer (as much as other numerical methods) from 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":"1811.08782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2018-11-21T15:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"5795231d307c5caf8a5046d13235baeb2e44961ccdabfde981167bbaa04ec766","abstract_canon_sha256":"9379d244919886851b40b1cb1f7ef26aae5bfbf812c5985e1197bcb3243b51e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:11.574215Z","signature_b64":"IYJq3RZtWxjn6PxddCEZTj60nS6IfWC8Y9gai0TPyu75DH8KHzA4RXY47u/iGYX+ZNB253pQGmxedSHZuqKVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e40fd5592874d8df25d18fd1b28361aef3100c3960bdebf1e05b60e3afea0682","last_reissued_at":"2026-05-18T00:00:11.573612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:11.573612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.CP","authors_text":"Adolfo Correia, Ali Al-Aradi, Danilo Naiff, Gabriel Jardim, Yuri Saporito","submitted_at":"2018-11-21T15:34:05Z","abstract_excerpt":"In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal execution, mean field games, etc. The main idea behind DGM is to represent the unknown function of interest using a deep neural network. A key feature of this approach is the fact that, unlike other commonly used numerical approaches such as finite difference methods, it is mesh-free. As such, it does not suffer (as much as other numerical methods) from the curse "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08782","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":""},"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":"1811.08782","created_at":"2026-05-18T00:00:11.573685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.08782v1","created_at":"2026-05-18T00:00:11.573685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08782","created_at":"2026-05-18T00:00:11.573685+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QH5KWJIOTMN","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QH5KWJIOTMN6JOR","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QH5KWJI","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2304.02180","citing_title":"Optimal Trading in Automated Market Makers with Deep Learning","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14493","citing_title":"Deep Learning for Solving and Estimating Dynamic Models in Economics and Finance","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2605.04307","citing_title":"A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation","ref_index":73,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3","json":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3.json","graph_json":"https://pith.science/api/pith-number/4QH5KWJIOTMN6JORR7I3FA3BV3/graph.json","events_json":"https://pith.science/api/pith-number/4QH5KWJIOTMN6JORR7I3FA3BV3/events.json","paper":"https://pith.science/paper/4QH5KWJI"},"agent_actions":{"view_html":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3","download_json":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3.json","view_paper":"https://pith.science/paper/4QH5KWJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.08782&json=true","fetch_graph":"https://pith.science/api/pith-number/4QH5KWJIOTMN6JORR7I3FA3BV3/graph.json","fetch_events":"https://pith.science/api/pith-number/4QH5KWJIOTMN6JORR7I3FA3BV3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3/action/storage_attestation","attest_author":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3/action/author_attestation","sign_citation":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3/action/citation_signature","submit_replication":"https://pith.science/pith/4QH5KWJIOTMN6JORR7I3FA3BV3/action/replication_record"}},"created_at":"2026-05-18T00:00:11.573685+00:00","updated_at":"2026-05-18T00:00:11.573685+00:00"}