MAGI: A Package for Inference of Dynamic Systems from Noisy and Sparse Data via Manifold-constrained Gaussian Processes

TL;DR

MAGI is a versatile software package that employs manifold-constrained Gaussian processes within a Bayesian framework to infer parameters and unobserved components of nonlinear dynamic systems from noisy, sparse data.

Contribution

It introduces a novel approach combining Gaussian processes and manifold constraints to handle unobserved system components in dynamic system inference.

Findings

Successfully infers parameters from noisy, sparse data

Handles unobserved components effectively

Available in R, MATLAB, and Python environments

Abstract

This article presents the MAGI software package for the inference of dynamic systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary differential equations with unknown parameters. While such models are widely used in science and engineering, the available experimental data for parameter estimation may be noisy and sparse. Furthermore, some system components may be entirely unobserved. MAGI solves this inference problem with the help of manifold-constrained Gaussian processes within a Bayesian statistical framework, whereas unobserved components have posed a significant challenge for existing software. We use several realistic examples to illustrate the functionality of MAGI. The user may choose to use the package in any of the R, MATLAB, and Python environments.