  Latent force models are a class of hybrid models for dynamic systems,
combining simple mechanistic models with flexible Gaussian process (GP)
perturbations. An extension of this framework to include multiplicative
interactions between the state and GP terms allows strong a priori control of
the model geometry at the expense of tractable inference. In this paper we
consider two methods of carrying out inference within this broader class of
models. The first is based on an adaptive gradient matching approximation, and
the second is constructed around mixtures of local approximations to the
solution. We compare the performance of both methods on simulated data, and
also demonstrate an application of the multiplicative latent force model on
motion capture data.
