Hosted by: Frank Alexander

In business analytics, operations research, engineering design, and other predictive sciences, a critical step in building models of reality and making predictions is solving an optimization problem. Linear and quadratic optimizers and penalties are a mainstay of data science, and have been popular due to their ability to handle large numbers of dimensions quickly. However, the use of linear and/or quadratic tools can seriously limit the amount and quality of information that can be applied in the inverse problem. One could argue that most real-world problems are probabilistic, high-dimensional, and nonlinear with nonlinear constraints — thus linear and quadratic tools may not actually be a good choice. Too often, we are forced to solve reduced-dimensional problems that may no longer adequately represent reality, but instead fit within the resource and design limitations of the selected optimizer. These limitations become much more pronounced when attempting to predict structure-property relationships in materials, as problems typically require significant computational resources, are nonlinear, and are often governed by rare-events. This talk will introduce some tools within the `mystic' framework for efficiently solving high-dimensional non-convex optimization problems with nonlinear constraints. We will, in the context of materials discovery, also discuss how `mystic', with the OUQ algorithm, can be used for rigorous model validation, certification, and the design of experiments.