Title: What Gaussian Process Latent Force Models Can Tell Us About Mechanical Systems?
Abstract: This talk will explore various ways that linear and nonlinear Gaussian process (GP) latent force models can be used to provide insight for problems encountered in mechanical systems. These problems include the inference of unmeasured loads acting on the mechanical system, which may have linear or nonlinear dynamics; the inference of the parameters of that system alongside the unknown loading; and learning of a nonlinear ordinary differential equation, the form of which is unknown a priori.  The essence of all of the approaches taken is to preserve, where possible, physical insight and structure within the model, while allowing unknown components to be flexibly modelled in a way that acknowledges and embraces the inherent uncertainty found in an engineering system. At the core of each model is the state-space representation of the GP in time which may be coupled with the mechanical system to provide a flexible machine learner as a representation of the unknown physical component. The physical structure in the model is encoded through a state-space representation of the known physical governing equations. Inference is then performed jointly over the state-space model for the states (physical and relating to the GP) and the parameters of the model.