Bayesian inference of ODEs with Gaussian processes

• URL: http://arxiv.org/abs/2106.10905v1
• Date: Mon, 21 Jun 2021 08:09:17 GMT
• Title: Bayesian inference of ODEs with Gaussian processes
• Authors: Pashupati Hegde, \c{C}a\u{g}atay Y{\i}ld{\i}z, Harri L\"ahdesm\"aki, Samuel Kaski, Markus Heinonen
• Abstract summary: We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.
• Score: 17.138448665454373
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.

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