Numerical Method for Parameter Inference of Nonlinear ODEs with Partial Observations

TL;DR

This paper introduces a novel method combining Gaussian process gradient matching and deterministic optimization for efficient parameter inference in nonlinear ODE systems with partial observations, addressing a common challenge in dynamical systems modeling.

Contribution

The paper presents a new approach that integrates FGPGM with deterministic optimization to improve accuracy and efficiency in parameter inference with limited observational data.

Findings

The method achieves high accuracy in parameter estimation.

It is computationally efficient with low sampling requirements.

The approach effectively handles partial observations in nonlinear ODEs.

Abstract

Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ODEs with partial observations. Our method combines fast Gaussian process based gradient matching (FGPGM) and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate and efficient.