  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.
