Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs

TL;DR

This paper introduces a novel Gaussian process-based gradient matching method for parameter identification in nonlinear ODE systems, providing a rigorous mathematical framework that enhances accuracy and computational efficiency.

Contribution

It presents a new interpretation of Gaussian process regression for dynamical systems, improving parameter inference accuracy without solving the ODEs explicitly.

Findings

Enhanced accuracy in parameter identification

Improved computational efficiency

Rigorous mathematical framework for Gaussian process methods

Abstract

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.