Learning sparse nonlinear dynamics via mixed-integer optimization
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11071_2022_Article_8178.pdf
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2.28 MB
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Adobe PDF
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230f3e39ade333e90f844d0709bb3d4f
Author(s)
Bertsimas, Dimitris
Gurnee, Wes
Date Issued
January 12, 2023
Publisher
Springer Netherlands
Citation
Bertsimas, Dimitris and Gurnee, Wes. 2023. "Learning sparse nonlinear dynamics via mixed-integer optimization."
Version
Final published version
Abstract
Abstract
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic sparse regression methods, has become a dominant tool for learning parsimonious models. We propose an exact formulation of the SINDy problem using mixed-integer optimization (MIO-SINDy) to solve the sparsity constrained regression problem to provable optimality in seconds. On a large number of canonical ordinary and partial differential equations, we illustrate the dramatic improvement in our approach in accurate model discovery while being more sample efficient, robust to noise, and flexible in accommodating physical constraints.
MIT Department
Sloan School of Management
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s11071-022-08178-9
