  Latent force models (LFMs) are flexible models that combine mechanistic
modelling principles (i.e., physical models) with non-parametric data-driven
components. Several key applications of LFMs need non-linearities, which
results in analytically intractable inference. In this work we show how
non-linear LFMs can be represented as non-linear white noise driven state-space
models and present an efficient non-linear Kalman filtering and smoothing based
method for approximate state and parameter inference. We illustrate the
performance of the proposed methodology via two simulated examples, and apply
it to a real-world problem of long-term prediction of GPS satellite orbits.
