MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics

TL;DR

MAGI-X is a neural network-based, manifold-constrained Gaussian process method that efficiently learns unknown system dynamics from data without domain knowledge or numerical integration, outperforming existing methods in accuracy and speed.

Contribution

It introduces MAGI-X, a novel non-parametric approach that circumvents numerical integration and handles partially observed systems for dynamic inference.

Findings

Achieves competitive accuracy in fitting and forecasting.

Significantly reduces computational time.

Handles partial observations effectively.

Abstract

Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and accurate data-driven method, MAGI-X, to learn the unknown dynamic from the observation data in a non-parametric fashion, without the need of any domain knowledge. Unlike the existing methods that mainly rely on the costly numerical integration, MAGI-X utilizes the powerful functional approximator of neural network to learn the unknown nonlinear dynamic within the MAnifold-constrained Gaussian process Inference (MAGI) framework that completely circumvents the numerical integration. Comparing against the state-of-the-art methods on three realistic examples, MAGI-X achieves competitive accuracy in both fitting and forecasting while only taking a fraction of computational time. Moreover, MAGI-X provides practical solution for the inference of partial observed systems, which no previous method is able to handle.