Learning ODE Models with Qualitative Structure Using Gaussian Processes

TL;DR

This paper introduces a data-efficient method for learning dynamical system models by integrating qualitative structural information with Gaussian Processes, enhancing extrapolation, stability, and reducing computational costs.

Contribution

It presents a novel approach that combines data with qualitative system information using sparse Gaussian Processes for improved dynamical system modeling.

Findings

Enhanced extrapolation performance

Improved long-term behavior of models

Reduced computational cost

Abstract

Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points. We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.