Causality and Bayesian network PDE for multiscale representations of porous media by Dr. Eric Hall

Overview

Abstract

Hierarchical porous media that feature properties and processes at multiple scales arise in many engineering applications including the design of novel materials for energy storage devices. Microscopic (pore-scale) properties of the media impact their macroscopic (continuum- or Darcy-scale) counterparts and understanding the relationships between processes on these two scales is essential for informing engineering decision tasks. However, microscopic properties typically exhibit complex statistical correlations that present challenges for the estimation of macroscopic quantities of interest (QoIs), e.g., global sensitivity analysis (GSA) of macroscopic QoIs with respect to microscopic material properties that respect structural constraints. We present a systematic framework for building correlations into stochastic multiscale models through Bayesian networks. This allows us to construct the joint probability density function (PDF) of model parameters through causal relationships that emulate engineering processes related to the design of hierarchical nanoporous materials. Such PDFs also serve as input for the forward propagation of parametric uncertainty; our findings indicate that the inclusion of causal relationships impacts predictions of macroscopic QoIs. To assess the impact of correlations and causal relationships between microscopic parameters on macroscopic material properties, we use a moment-independent GSA based on the differential mutual information. Our GSA accounts for the correlated inputs and complex non-Gaussian QoIs. The global sensitivity indices are used to rank the effect of uncertainty in microscopic parameters on macroscopic QoIs, to quantify the impact of causality on the multiscale model's predictions, and to provide physical interpretations of these results for hierarchical nanoporous materials.

Brief Biography

A native of Philadelphia, Eric Hall earned his Ph.D. in Mathematics and Statistics at the University of Edinburgh in 2013. Eric has held postdoctoral appointments in Numerical Analysis at KTH Royal Institute of Technology and in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. Presently, Eric is a postdoctoral research scientist in the newly formed Chair of Mathematics for Uncertainty Quantification at RWTH Aachen University. Eric’s research interests include stochastic and predictive modeling, uncertainty quantification, and applied probability.

Light refreshments will be served around 1:45 PM