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Computing the distribution of trajectories from a Gaussian Process model of adynamical system is an important challenge in utilizing such models. Motivatedby the computational cost of sampling-based approaches, we considerapproximations of the model's output and trajectory distribution. We show thatprevious work on uncertainty propagation, focussed on discrete state-spacemodels, incorrectly included an independence assumption between subsequentstates of the predicted trajectories. Expanding these ideas to continuousordinary differential equation models, we illustrate the implications of thisassumption and propose a novel piecewise linear approximation of GaussianProcesses to mitigate them.

The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models