  Physically-inspired latent force models offer an interpretable alternative to
purely data driven tools for inference in dynamical systems. They carry the
structure of differential equations and the flexibility of Gaussian processes,
yielding interpretable parameters and dynamics-imposed latent functions.
However, the existing inference techniques associated with these models rely on
the exact computation of posterior kernel terms which are seldom available in
analytical form. Most applications relevant to practitioners, such as Hill
equations or diffusion equations, are hence intractable. In this paper, we
overcome these computational problems by proposing a variational solution to a
general class of non-linear and parabolic partial differential equation latent
force models. Further, we show that a neural operator approach can scale our
model to thousands of instances, enabling fast, distributed computation. We
demonstrate the efficacy and flexibility of our framework by achieving
competitive performance on several tasks where the kernels are of varying
degrees of tractability.
