# Structured model selection via ℓ1-ℓ2 optimization

arXiv: https://arxiv.org/abs/2305.17467 · HTML: https://mlsanity.com/paper/2305.17467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 27 May 2023.

## Abstract (arXiv)

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. 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.