{"paper":{"title":"Data-Adaptive Learning of Dynamical Systems by Matching Transfer Operators and Invariant Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS"],"primary_cat":"math.NA","authors_text":"Jonah Botvinick-Greenhouse, Yinong Huang, Yunan Yang","submitted_at":"2026-07-01T03:34:21Z","abstract_excerpt":"Trajectory-based learning of dynamical systems is often fragile in the presence of noise, chaos, or sparse observations, as small pointwise errors can rapidly amplify. We introduce a transition-statistics approach to system identification that learns dynamics by matching the induced motion of probability mass across a data-adaptive mesh. Given trajectory data, we build an unstructured partition of state space and approximate the Perron--Frobenius operator with a regularized Ulam transition matrix. We replace hard cell indicators with continuous, piecewise-smooth partition-of-unity weights, yie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00391","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00391/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"}