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.

翻译：高效建模高度非线性动力系统中的现象，同时精确量化不确定性是一项具有挑战性的任务，通常需要针对特定问题的技术。我们提出深度隐式力模型（DLFM），这是一种解决该问题的领域无关方法，其核心是深度高斯过程架构，其中每层的核函数基于过程卷积框架从常微分方程导出。我们提出了两种不同形式的DLFM，分别利用权重空间和基于变分诱导点的高斯过程近似，两者均适用于双随机变分推断。实验证明，我们的模型能够捕捉真实世界多变量时间序列数据中的高度非线性行为。此外，我们发现该方法在基准回归任务上取得了与多种概率模型相当的性能。我们还通过实证评估了诱导点框架对基于LFM模型外推能力的负面影响。