From forward simulation to the outer loop

Why are optimization, inversion and UQ important?

Optimization, inversion and UQ are the key mathematical and computational tasks in what is often referred to as the “outer loop” (i.e., computational applications that form outer loops around a forward model).

Optimization A significant aspect of the field of CSE is the development of theory and methods for optimizing systems governed by large-scale CSE models, typically involving systems of ODEs or PDEs. Such problems are prevalent in applications of optimal control, optimal design and optimal experimental design.

Inversion In general, any endeavor to infer cause from effect — to extract knowledge from data — can be viewed as an inverse problem. Inverse problems sit at the heart of discovery and innovation in every area of science, engineering and medicine. As just a few examples of model-based inverse problems, we may infer: coalescing binary system properties from detected gravitational waves, earth structure from reflected seismic waves, reaction rates from measurements of chemically reacting flows, ice sheet basal friction from satellite observations of surface flow, and three-dimensional bone structure from X-ray computed tomography measurements.

Bayesian inversion for improving the understanding of the role of the global ocean, sea ice and the polar ice sheets in the climate system

Bayesian Inversion for Oil Spills: Developing a framework to pinpoint the origin of oil spills by constructing a probability distribution of where the origin may be located. Above: a simulation of the Deepwater Horizon oil spill using a newly developed particle tracking code.

Uncertainty quantification (UQ) involves the quantitative characterization and management of uncertainty in a broad range of applications. It employs both computational models and observational data, together with theoretical analysis. UQ encompasses many different tasks, including uncertainty propagation, sensitivity analysis, statistical inference and model calibration, decision making under uncertainty, experimental design and model validation.

Surrogate, reduced-order and multifidelity modeling to accelerate UQ for large-scale complex systems