Research interests

Our research is focused on machine learning and uncertainty quantification with applications in the sciences and engineering. The underlying models, if they exist, are partial differential equations (PDE). In uncertainty quantification, we use stochastic partial differential equations to model and to simulate process variations, fluctuations, noise, etc. Another field of expertise in uncertainty quantification is optimal Bayesian PDE inversion, which makes it possible to calculate the probability distributions of quantities of interest. Applications in the sciences and engineering include nanotechnology and sensors. In machine learning, we develop reinforcement-learning algorithms and the underlying theory with a focus on quantifying risk and uncertainties in strategies. Applications include optimal medical treatments, optimal control of devices such as sensors, and autonomous driving.