  Latent force models are systems whereby there is a mechanistic model
describing the dynamics of the system state, with some unknown forcing term
that is approximated with a Gaussian process. If such dynamics are non-linear,
it can be difficult to estimate the posterior state and forcing term jointly,
particularly when there are system parameters that also need estimating. This
paper uses black-box variational inference to jointly estimate the posterior,
designing a multivariate extension to local inverse autoregressive flows as a
flexible approximater of the system. We compare estimates on systems where the
posterior is known, demonstrating the effectiveness of the approximation, and
apply to problems with non-linear dynamics, multi-output systems and models
with non-Gaussian likelihoods.
