论文标题
部分可观测时空混沌系统的无模型预测
The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models
论文作者
论文摘要
从动态系统的高斯过程模型中计算轨迹的分布是利用此类模型的重要挑战。由基于抽样的方法的计算成本激励，我们考虑了模型的输出和轨迹分布的近似值。我们表明，以前关于不确定性传播的工作着重于离散的状态空间模型，错误地包括了预测轨迹的后续状态之间的独立性假设。将这些想法扩展到连续的普通微分方程模型，我们说明了该假设的含义，并提出了高斯过程的新型分段线性近似来减轻它们。
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.
