Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations of the model's output and trajectory distribution. We show that previous work on uncertainty propagation, focussed on discrete state-space models, incorrectly included an independence assumption between subsequent states of the predicted trajectories. Expanding these ideas to continuous ordinary differential equation models, we illustrate the implications of this assumption and propose a novel piecewise linear approximation of Gaussian Processes to mitigate them.

翻译：计算动态系统高斯过程模型轨迹的分布是利用此类模型的重要挑战。受基于采样的方法计算成本的启发，我们考虑了模型输出和轨迹分布的近似方法。我们证明，先前针对离散状态空间模型的不确定性传播研究，错误地假设预测轨迹的后续状态之间相互独立。将这些思想扩展到连续的常微分方程模型，我们阐释了该假设的含义，并提出一种新颖的高斯过程分段线性近似方法来缓解这些问题。