Research Thrust 1

LEARNING COMPLEX PREDICTIVE MODELS FROM DATA
VIA BAYESIAN INFERENCE AND OPTIMIZATION

The problem of how data can be used to optimally inform predictive models of complex systems is at its core an inverse problem. Bayesian inference provides a rational framework for learning from data through the lens of physics-based models under both data and model uncertainty. However, full solution of the Bayesian inference problem remains out of reach for large scale complex models in high parameter dimensions. Moreover, in many cases the physics model is unavailable or unreliable, and a predictive model must be inferred from data.

The explosive growth of machine learning has resulted in new data-driven representations and stochastic optimization algorithms. Integrating these new advances with classical inverse theory algorithms that are able to respect physics constraints in a rigorous and principled way paves the way to overcoming the challenges presented by learning optimal models from data for complex uncertain systems.

Research Thrust 2

OPTIMIZING EXPERIMENTS, PROCESSES, AND DESIGNS UNDER UNCERTAINTY

Once predictive models are learned from data under uncertainty, we are in a position to optimize these uncertain models with the goal of maximizing system performance while minimizing resource use. Two optimization settings arise. The first addresses the question of how to optimally steer experiments (either physical or computational) to minimize the uncertainty in inferred models or maximize the information gained. The resulting Bayesian optimal experimental design (BOED) problem presents enormous mathematical and computational challenges: the Bayesian inverse problem—challenging as it is—is just a subproblem within the outer OED optimization problem.

The second optimization setting builds on the uncertain models that have been inferred from data generated from optimized experiments to address what is often the ultimate goal of modeling and simulation: optimal control or design of complex uncertain systems. Optimal control under uncertainty subsumes a challenging subproblem: just determining the objective function and constraints (which depend on random variables) requires forward propagation of uncertainty through a complex model. The optimization problem—iterating the controls toward optimality driven by gradient information—is then much more difficult than forward UQ.