Physics based approaches to data modeling involve constructing an accurate mechanistic model of data, often based on differential equations. Statistical and machine learning approaches are typically data driven—perhaps through regularized function approximation.
These two approaches to data modeling are often seen as polar opposites, but in reality they are two different ends to a spectrum of approaches we might take. Physics based approaches can be seen as strongly mechanistic, the mechanistic assumptions are hard encoded into the model. Data-driven approaches do incorporate assumptions that might be seen as being derived from some underlying mechanism, such as smoothness. In this sense they are weakly mechanistic.
In this talk we introduce latent force models. Latent force models are a new approach to data representation that model data through unknown forcing functions that drive differential equation models. By treating the unknown forcing functions with Gaussian process priors we can create probabilistic models that exhibit particular physical characteristics of interest, for example, in dynamical systems resonance and inertia. This allows us to perform a synthesis of the data driven and physical modeling paradigms. A moderately mechanistic approach. We show an application in modelling of human motion capture data.