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.

翻译：最近的机器学习进步建议直接从数据中对未知连续时间系统动态进行黑箱估计,然而,早期的工程是以近似ODE解决方案或点估计为基础的。我们提出了一种新颖的Bayesian非参数模型,利用Gaussian过程直接从数据中推断未知ODE系统的子孙。我们从分解功能抽样中得出微小的变异推论,以代表矢量场子孙。我们还引入了概率射击增强法,以便能够从任意的长轨道中有效地推断出。该方法展示了计算矢量场子孙的益处,预测的不确定性比多个ODE学习任务的其他方法分得分多。