Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes

TL;DR

This paper introduces MAGI, a Bayesian Gaussian process-based method for efficient inference of nonlinear dynamic systems from noisy, sparse data, bypassing numerical integration and handling unobserved components.

Contribution

MAGI is a novel manifold-constrained Gaussian process approach that improves speed and accuracy in parameter estimation for ODE-based models with noisy, sparse data.

Findings

MAGI achieves faster inference than traditional methods.

MAGI accurately estimates parameters in physical experiments.

MAGI handles unobserved system components effectively.

Abstract

Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data is a vital task in many fields. We propose a fast and accurate method, MAGI (MAnifold-constrained Gaussian process Inference), for this task. MAGI uses a Gaussian process model over time-series data, explicitly conditioned on the manifold constraint that derivatives of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. MAGI is also suitable for inference with unobserved system components, which often occur in real experiments. MAGI is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of MAGI using realistic examples based on physical experiments.