{"paper":{"title":"Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.OC"],"primary_cat":"math.NA","authors_text":"Alex Massucco, Carlos Esteve-Yag\\\"ue, Richard Tsai","submitted_at":"2024-06-15T23:18:26Z","abstract_excerpt":"We present a simple algorithm to approximate the viscosity solution of Hamilton-Jacobi (HJ) equations by means of an artificial deep neural network. The algorithm uses a stochastic gradient descent-based method to minimize the least square principle defined by a monotone, consistent numerical scheme. We analyze the least square principle's critical points and derive conditions that guarantee that any critical point approximates the sought viscosity solution. The use of a deep artificial neural network on a finite difference scheme lifts the restriction of conventional finite difference methods"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10758","kind":"arxiv","version":4},"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/2406.10758/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"}