Learning unknown ODE models with Gaussian processes

TL;DR

This paper introduces a nonparametric approach using Gaussian processes to learn unknown differential equations directly from data, enabling modeling of complex systems without predefined equations.

Contribution

It presents a novel Gaussian process-based framework for learning continuous-time dynamics without prior knowledge of the underlying equations.

Findings

Successfully infers dynamics from sparse data

Accurately simulates future system behavior

Handles arbitrary continuous-time systems

Abstract

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future.