McDonald, T.M. and Álvarez, M.A. (Submitted: 2021) Compositional modeling of nonlinear dynamical systems with ODE-based random features. arXiv. (Submitted)
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). For reuse permissions, please contact the Author(s). |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council EP/R034303/1; EP/T00343X/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Jun 2021 09:01 |
Last Modified: | 30 Jun 2021 09:01 |
Published Version: | https://arxiv.org/abs/2106.05960 |
Status: | Submitted |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175743 |