Learning sparse nonlinear dynamics via mixed-integer optimization

Abstract Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification nonlinear dynamics (SINDy) framework, powered by heuristic regression methods, has become dominant tool for learning parsimonious models. We propose an exact formulation SINDy using mixed-integer optimization (MIO-SINDy) to solve sparsity constrained provable optimality seconds. On large number canonical ordinary and partial differential equations, we illustrate dramatic improvement our approach accurate model discovery while being more sample efficient, robust noise, flexible accommodating physical constraints.