Variational multiple shooting for Bayesian ODEs with Gaussian processes
This addresses the challenge of learning ODE dynamics with uncertainty quantification for applications in fields like physics or biology, though it appears incremental by building on prior black-box estimation approaches.
The paper tackled the problem of estimating unknown continuous-time system dynamics from data by proposing a Bayesian nonparametric model using Gaussian processes to infer posteriors of ODE systems, resulting in predictive uncertainty scores that outperform alternative methods on multiple ODE learning tasks.
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.