{"paper":{"title":"Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CE","cs.LG","cs.NA","math.DS","math.NA"],"primary_cat":"math.OC","authors_text":"Alireza Doostan, Conor Rowan, Grant Norman, Kurt Maute","submitted_at":"2026-02-13T22:44:33Z","abstract_excerpt":"In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and its gradient, we leverage trajectory data on the optimization variables to learn the continuous-time dynamics associated with gradient descent, Newton's method, and ADAM optimization. The discovered gradient flows are then solved as a surrogate for the original optimization problem. To this end, we introduce the Learned Gradient Flow (LGF) optimizer, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.13513","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/2602.13513/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"}