This repository contains a PyTorch implementation of the deep latent force model (DLFM), presented in the paper, Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features, published at NeurIPS 2021.
The DLFM takes the form of a deep Gaussian process with random feature expansions, but with the random Fourier features in question derived from a physics-informed ODE1 LFM kernel, rather than a more general choice (such as the exponentiated quadratic kernel).
These compositions of physics-informed random features allow us to model nonlinearities in multivariate dynamical systems with a sound quantification of uncertainty and the ability to extrapolate effectively. The plot below shows DLFM predictions on a highly nonlinear multivariate time series, extracted from the CHARIS PhysioNet dataset; note the ability of the model to extrapolate beyond the training regime which ends at t=0.7.
requirements.txt
contains the small list of packages required to run toy_demo.py
, which is identical to the toy data scenario described in our paper.
@inproceedings{mcdonald2021compositional,
title={Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features},
author={McDonald, Thomas M and {\'A}lvarez, Mauricio A},
booktitle={Advances in Neural Information Processing Systems},
year={2021}
}