Structured model selection via ℓ1−ℓ2 optimization

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 ℓ1−ℓ2 sparse optimization solved by the alternating direction method of multipliers. 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 number of candidate functions.