{"paper":{"title":"Revealing dynamics of non-autonomous complex systems from data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A data-driven method discovers governing equations for non-autonomous systems by selecting optimal basis functions from a library.","cross_cats":["math.DS","physics.data-an"],"primary_cat":"nlin.CD","authors_text":"Chengzuo Zhuge, Wei Chen, Zhefan Xu, Zheng Jiang","submitted_at":"2026-05-10T09:20:55Z","abstract_excerpt":"Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing challenge due to the inherent non-autonomicity and unknowability of the underlying dynamics. Here, we introduce a data-driven approach for inferring non-autonomous dynamical equations by identifying an optimal set of basis functions within the model space, enabling the reconstruction of complex systems behavior under simplified prior specifications. Our method demo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our method demonstrates effectiveness in equation discovery on canonical synthetic systems such as cusp bifurcation and coupled Kuramoto oscillators. Furthermore, we extend the application of this approach to leaf cellular energy, unmanned aerial vehicle navigation, chick-heart aggregates, and marine fish community under simple basis function libraries.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The true non-autonomous dynamics can be accurately represented by a sparse linear combination of functions drawn from a user-supplied basis library, and that an optimal subset can be identified under simplified prior specifications.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A data-driven framework discovers non-autonomous dynamical equations from data via optimal basis function selection, shown effective on synthetic systems and applied to biological and engineering examples.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A data-driven method discovers governing equations for non-autonomous systems by selecting optimal basis functions from a library.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b33a06cad28a70d4b01346ac4cf60826afed4e5ab483bd1da667e1242c44bd78"},"source":{"id":"2605.13878","kind":"arxiv","version":1},"verdict":{"id":"499dd9c4-001f-4cb7-a316-0c64926777ef","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:45:36.652640Z","strongest_claim":"Our method demonstrates effectiveness in equation discovery on canonical synthetic systems such as cusp bifurcation and coupled Kuramoto oscillators. Furthermore, we extend the application of this approach to leaf cellular energy, unmanned aerial vehicle navigation, chick-heart aggregates, and marine fish community under simple basis function libraries.","one_line_summary":"A data-driven framework discovers non-autonomous dynamical equations from data via optimal basis function selection, shown effective on synthetic systems and applied to biological and engineering examples.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The true non-autonomous dynamics can be accurately represented by a sparse linear combination of functions drawn from a user-supplied basis library, and that an optimal subset can be identified under simplified prior specifications.","pith_extraction_headline":"A data-driven method discovers governing equations for non-autonomous systems by selecting optimal basis functions from a library."},"references":{"count":66,"sample":[{"doi":"","year":2017,"title":"De Col, V.et al.Atp sensing in living plant cells reveals tissue gradients and stress dynamics of energy physiology.Elife6, e26770 (2017). 21","work_id":"966802a9-e003-4c7c-bd41-fa3e848b91c0","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Wagner, S.et al.Multiparametric real-time sensing of cytosolic physiology links hypoxia responses to mitochondrial electron transport.New Phytologist224, 1668– 1684 (2019)","work_id":"6816813b-1906-424b-a33d-b308067966f7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"Influence of water flow, water temperature and light on fish migration in rivers.Nordic Journal of Freshwater Research66, 20–35 (1991)","work_id":"0c080c23-7cdc-4389-938f-31e81118df2f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Marra, P. P., Francis, C. M., Mulvihill, R. S. & Moore, F. R. The influence of climate on the timing and rate of spring bird migration.Oecologia142, 307–315 (2005)","work_id":"0a93c214-060c-4150-ab16-f504a027b700","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"In IEEE Intelligent Vehicles Symposium, 163–168 (IEEE, 2011)","work_id":"a0ceeb91-cd6b-4719-85be-282d89d5b686","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":66,"snapshot_sha256":"c8d01224c3d70c166e2f11382de53c1cbf25f3f67e460abd5bf8723a214309f0","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"95c3a70b6af156e753013b5a850c88f6d7856615ca9efb00e380374125ea712f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}