CEE Seminar: Data-Driven probabilistic Learning on Manifolds and Nonconvex Optimization Problems with Afpplications

The talk will be devoted to the presentation of a novel approach concerning data-driven probabilitistic learning on manifolds with applications in computational mechanics. This tool of the computational statistics can be viewed as a useful method in scientific machine learning based on the probability theory. We first explaining the concept/method of this probabilistic learning on manifolds by discussing a challenging problem of nonconvex optimization under uncertainties (OUU). We will then present the mathematical formulation and the main steps of the method based on the construction of a diffusion-maps basis and the projection on it of a nonlinear Itô stochastic differential equation. After having presented two simple illustrations, fours applications will be presented:
-Optimization under uncertainties using a limited number of function evaluations.
-Enhancing model predictability for a scramjet using probabilistic learning on manifolds.
-Design optimization under uncertainties of a mesoscale implant in biological tissues using probabilistic learning.
-Probabilistic learning onmanifolds for nonparametric probabilistic approach of model-form uncertainties in nonlinear computational mechanics.