Structured model selection via $\ell_1-\ell_2$ optimization

• URL: http://arxiv.org/abs/2305.17467v2
• Date: Tue, 30 May 2023 00:54:10 GMT
• Title: Structured model selection via $\ell_1-\ell_2$ optimization
• Authors: Xiaofan Lu, Linan Zhang and Hongjin He
• Abstract summary: We develop a learning approach for identifying structured dynamical systems. We show that if the set of candidate functions forms a bounded system, the recovery is stable and is bounded.
• Score: 1.933681537640272
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is performed by a sparse least-squares fitting over a large set of candidate functions via a nonconvex $\ell_1-\ell_2$ sparse optimization solved by the alternating direction method of multipliers. Using a Bernstein-like inequality with a coherence condition, we show that if the set of candidate functions forms a structured random sampling matrix of a bounded orthogonal system, the recovery is stable and the error is bounded. The learning approach is validated on synthetic data generated by the viscous Burgers' equation and two reaction-diffusion equations. The computational results demonstrate the theoretical guarantees of success and the efficiency with respect to the ambient dimension and the number of candidate functions.

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