Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a domain-agnostic model to address this issue termed the deep latent force model (DLFM), a deep Gaussian process with physics-informed kernels at each layer, derived from ordinary differential equations 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 present empirical evidence of the capability of the DLFM to capture the dynamics present in highly nonlinear real-world multi-output time series data. Additionally, we find that the DLFM is capable of achieving comparable performance to a range of non-physics-informed probabilistic models on benchmark univariate regression tasks. We also empirically assess the negative impact of the inducing points framework on the extrapolation capabilities of LFM-based models.

翻译：对高度非线性动态系统行为进行建模并实现稳健的不确定性量化是一项极具挑战性的任务，通常需要针对具体问题专门设计的方法。本文提出了一种通用领域模型——深度隐式力模型（DLFM），它是一种具有物理信息核函数的深度高斯过程，每层核函数均通过过程卷积框架从常微分方程推导而来。我们提出了两种不同的DLFM公式，分别利用权重空间和变分诱导点的高斯过程近似，这两种方法均适用于双随机变分推断。实验证明，DLFM能够有效捕获高度非线性真实世界多输出时间序列数据中的动态特性。此外，我们在基准单变量回归任务上发现，DLFM可达到与一系列非物理信息概率模型相当的性能。同时，我们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。