Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features

TL;DR

This paper introduces a novel, domain-agnostic method for modeling highly nonlinear dynamical systems using compositions of physics-informed random features derived from ODEs, enabling uncertainty quantification.

Contribution

It proposes a new approach combining random features, deep Gaussian processes, and variational inference for nonlinear dynamical systems modeling.

Findings

Captures highly nonlinear behavior in real-world data

Achieves performance comparable to existing probabilistic models on benchmarks

Provides effective uncertainty quantification

Abstract

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic approach to tackling this problem, using compositions of physics-informed random features, derived from ordinary differential equations. The architecture of our model leverages recent advances in approximate inference for deep Gaussian processes, such as layer-wise weight-space approximations which allow us to incorporate random Fourier features, and stochastic variational inference for approximate Bayesian inference. We provide evidence that our model is capable of capturing highly nonlinear behaviour in real-world multivariate time series data. In addition, we find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks.