Simultaneous model discovery and state estimation under high data corruption

Abstract

This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated likelihood function. Sparsity is enforced by a selection algorithm which iteratively removes terms and compares models using statistical information criteria. Large scale optimization is performed using a second-order variant of the Levenberg-Marquardt method, where the gradient and Hessian are computed via automatic differentiation. The proposed method is illustrated and tested on several systems with varying levels of noisy and incomplete data. Comparisons are made to a state-of-the-art algorithm for system identification, demonstrating competitiveness of the proposed approach.