Structured model selection via $\ell_1-\ell_2$ optimization
This work addresses automated model selection for structured dynamical systems, which is incremental as it builds on existing sparse optimization methods with theoretical guarantees.
The paper tackles the problem of identifying structured dynamical systems from undersampled and noisy spatiotemporal data by developing a learning approach based on nonconvex ℓ1-ℓ2 sparse optimization, showing stable recovery with bounded error and validating it on synthetic data from equations like the viscous Burgers' equation.
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.