His research includes using applied mathematics and computational science to enhance autonomous decision making under uncertainty. His research has an emphasis on controlling systems that must act in complex environments that are often represented through expensive computational simulations. His research uses tools from wide ranging areas including uncertainty quantification, statistical inference, machine learning, numerical analysis, function approximation, control, and optimization. Several of the key areas he focuses on are: optimal planning by solving large scale Markov decision processes, fast Bayesian estimation for nonlinear dynamical systems, high-dimensional compression and approximation of physical quantities of interest, and fusion of information from varying simulation fidelities and data through multi-fidelity modeling.