Manifold sampling for data-driven UQ and optimization (Keynote lecture presented by R. Ghanem)
Abstract
We describe a new methodology for constructing probability measures from observations in high-dimensional space. A typical challenge with standard procedures for similar problems is the growth of the required number of samples with the dimension of the ambient space. The new methodology first delineates a manifold in a space spanned by available samples, then it constructs a probability distribution on that manifold together with a projected Ito equation for sampling from that distribution. A demonstration of this new methodology to problems in uncertainty quantification, and in design optimization under uncertainty will be shown.