Deep Latent Force Models

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 (view arXiv preprint here), which has been accepted to 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.

Usage

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.

Citation

@misc{mcdonald2021compositional,
      title={Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features}, 
      author={Thomas M. McDonald and Mauricio A. Álvarez},
      year={2021},
      eprint={2106.05960},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}