  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.
