期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2021.0201
关键词
scientific machine learning; dynamical systems; uncertainty quantification; model discovery
资金
- DOE [DE-SC0019116]
- AFOSR [FA9550-20-1-0060]
- DOE-ARPA [DE-AR0001201]
- NSF [EIA-0196217]
- U.S. Department of Energy (DOE) [DE-SC0019116] Funding Source: U.S. Department of Energy (DOE)
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 utilizes differentiable programming to propagate gradient information and performs Bayesian inference with Hamiltonian Monte Carlo sampling and Gaussian Process priors, allowing for the exploitation of temporal correlations in observed data and efficient inference of posterior distributions over plausible models.
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'.
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