Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features
This addresses the problem of uncertainty-aware modeling in nonlinear dynamics for researchers and practitioners, but it appears incremental as it builds on existing techniques like deep Gaussian processes.
The paper tackled modeling highly nonlinear dynamical systems with uncertainty quantification by introducing a domain-agnostic approach using compositions of physics-informed random features from ODEs, achieving comparable performance to other probabilistic models on benchmark tasks.
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.