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This research introduces an active learning strategy that significantly reduces data requirements for identifying governing equations in complex dynamical systems by iteratively sampling informative regions. By extending the E-SINDy framework with epistemic uncertainty estimation, the method effectively handles both ODEs and PDEs, including challenging cases like shock fronts and spatially complex landscapes. The approach offers a practical solution for scenarios where data acquisition is expensive, enabling accurate model discovery with minimal sample sizes.
How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit
arXiv:2606.12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions. However, data acquisition in real-world settings is often expensive. This work addresses this challenge by introducing an active learning strategy for dynamics discovery in the ultra-low data limit. Rather than sampling randomly, our method iteratively prioritizes regions that are most informative for model identification. This approach builds on Sparse Identification of Nonlinear Dynamics (SINDy), and utilizes an ensemble extension, E-SINDy, to estimate epistemic uncertainty and guide the sampling for both ordinary and partial differential equations (ODEs/PDEs). For ODEs, an exhaustive analysis is conducted on the Lorenz system across varying data budgets and noise levels. For PDEs, two systems with contrasting dynamical characteristics are examined: the Burgers' equation, where a sharp shock front creates a distinction between informative and uninformative regions, and the Kuramoto-Sivashinsky equation, which presents a more spatially complex sampling landscape. Across all scenarios, the proposed method accurately identifies the governing dynamics with significantly fewer data samples than random sampling.
Title:How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit
Abstract:Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions. However, data acquisition in real-world settings is often expensive. This work addresses this challenge by introducing an active learning strategy for dynamics discovery in the ultra-low data limit. Rather than sampling randomly, our method iteratively prioritizes regions that are most informative for model identification. This approach builds on Sparse Identification of Nonlinear Dynamics (SINDy), and utilizes an ensemble extension, E-SINDy, to estimate epistemic uncertainty and guide the sampling for both ordinary and partial differential equations (ODEs/PDEs). For ODEs, an exhaustive analysis is conducted on the Lorenz system across varying data budgets and noise levels. For PDEs, two systems with contrasting dynamical characteristics are examined: the Burgers' equation, where a sharp shock front creates a distinction between informative and uninformative regions, and the Kuramoto-Sivashinsky equation, which presents a more spatially complex sampling landscape. Across all scenarios, the proposed method accurately identifies the governing dynamics with significantly fewer data samples than random sampling.
Machine Learning (cs.LG); Dynamical Systems (math.DS); Optimization and Control (math.OC)
arXiv:2606.12182 [cs.LG]
(or arXiv:2606.12182v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.12182 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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