Overview
My research is focused on learning generalizable models of dynamical systems from sparse and noisy data. This problem is challenging because datasets with these characteristics induce high estimation uncertainty that can easily lead to overfitting and overconfidence. Addressing this challenge requires proper modeling and quantification of the model, measurement, and parameter uncertainties that enter into the parametric system identification (ID) problem. Many existing system ID approaches, however, will only model one or two of these uncertainties for the sake of computational ease. As a result, these methods often require training datasets with tens to hundreds of thousands of data points to produce accurate estimates. For many engineering applications, however, collecting datasets of these sizes is not a feasible option, and an alternative methodology is needed.
To enable robust system ID under high uncertainty, I seek to develop a computational Bayesian framework that draws on the fields of applied probability, machine learning, and engineering physics. This framework will be realized through research into the following topics:
- probabilistic modeling of complex scientific problems,
- incorporation of scientific knowledge into the system ID framework,
- efficient and scalable evaluation and sampling of posterior distributions.