Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We outline the deep latent force model (DLFM), a domain-agnostic approach to tackling this problem, which consists of a deep Gaussian process architecture where the kernel at each layer is derived from an ordinary differential equation using the framework of process convolutions. Two distinct formulations of the DLFM are presented which utilise weight-space and variational inducing points-based Gaussian process approximations, both of which are amenable to doubly stochastic variational inference. We provide evidence that our model is capable of capturing highly nonlinear behaviour in real-world multivariate time series data. In addition, we find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks. We also empirically assess the negative impact of the inducing points framework on the extrapolation capabilities of LFM-based models.

本研究提出了深度潜在力模型（DLFM），它是一种面向领域的方法，用于准确建模高度非线性动力系统并量化不确定性，该模型采用深度高斯过程架构，每个层的核函数基于普通微分方程和过程卷积的框架导出，通过权重空间和变分感应点的高斯过程近似，我们证明了该模型能够捕捉真实世界多元时间序列数据中的高度非线性行为，并且在基准回归任务上与其他概率模型具有可比性能，同时我们还通过实证评估证明了感应点框架对基于LFM的模型的外推能力的负面影响。

深层潜在力模型：基于 ODE 的过程卷积用于贝叶斯深度学习