Simultaneous model discovery and state estimation under high data corruption

TL;DR

This paper introduces a robust sparse regression method for discovering differential equations from noisy, incomplete data, simultaneously estimating models and states with high accuracy and efficiency.

Contribution

It presents a novel approach combining sparse regression, statistical model selection, and large-scale optimization for system identification under challenging data conditions.

Findings

Effective in high noise and data incompleteness scenarios

Competitive with existing state-of-the-art algorithms

Demonstrates accurate model discovery and state estimation

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.