Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data
- Department of Mechanical Engineering, and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.
- Research Organization:
- Raytheon Technologies Corp., Waltham, MA (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)
- Sponsoring Organization:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)
- DOE Contract Number:
- AR0001201; SC0019116
- OSTI ID:
- 1979597
- Journal Information:
- Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2229; ISSN 1364-503X
- Publisher:
- The Royal Society Publishing
- Country of Publication:
- United States
- Language:
- English
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