{"paper":{"title":"Data-driven reconstruction of dynamical systems using Takens' Theorem, manifold learning, and universal function approximators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Andrew L. Ferguson, Maximilian Topel","submitted_at":"2026-08-05T23:50:13Z","abstract_excerpt":"Embedding theorems can be used to provide theoretical guarantees about the relation between low-dimensional observations of a system and its full-dimensional state and dynamics. Such theorems do not, however, provide guidance on observable choice, embedding construction, or methodologies to learn the mapping between the embedding and full-dimensional state. In this work, we develop an algorithmic framework, TAkens Reconstruction (TAR), to analyze and reconstruct arbitrary dynamical systems from low-dimensional time series using an integration of Takens' Delay Embedding Theorem, manifold learni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05477","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/2608.05477/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"}