Not yet reviewed by Pith; the record is open.

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.