Speaker
Description
Propagating uncertainty from a potentially large number of random inputs through a computational model is becoming increasingly challenging due to the high cost of evaluating complex simulations. Stratified sampling is a well-known variance reduction strategy that, however, has mainly been employed in low-dimensional applications because of the difficulty of extending it to high-dimensional settings. In this talk, we propose using a recently introduced nonlinear dimensionality reduction approach, neural active manifolds (NeurAM), to enable stratified sampling in high dimensions. We leverage autoencoders to discover a one-dimensional manifold that captures most of the variability of the model output, aided by a simultaneously learned surrogate model whose inputs lie on this manifold. We then use the discovered neural active manifold to project a one-dimensional stratification back into the original input space, generating partitions that tend to follow the level sets of the model.