Mutual Information for Explainable Deep Learning of Multiscale Systems

TL;DR

This paper introduces a model-agnostic, mutual information-based global sensitivity analysis method using neural network surrogates to efficiently identify influential variables in complex, high-dimensional systems, aiding accelerated design and optimization.

Contribution

It develops a novel, differential mutual information approach for global sensitivity analysis that is compatible with black-box models and leverages neural network surrogates for efficiency.

Findings

Effective ranking of control variables in energy storage applications.

Demonstrated usefulness of the method in complex, high-dimensional systems.

Provides a framework for accelerated product design and optimization.

Abstract

Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated control variables (CVs) and quantities of interest (QoIs) with non-Gaussian and possibly multimodal distributions. We develop a model-agnostic, moment-independent global sensitivity analysis (GSA) that relies on differential mutual information to rank the effects of CVs on QoIs. The data requirements of this information-theoretic approach to GSA are met by replacing computationally intensive components of the physics-based model with a deep neural network surrogate. Subsequently, the GSA is used to explain the network predictions, and the surrogate is deployed to close design loops. Viewed as an uncertainty quantification method for interrogating the surrogate, this framework is compatible with a wide variety of black-box models. We demonstrate that the surrogate-driven mutual information GSA provides useful and distinguishable rankings on two applications of interest in energy storage. Consequently, our information-theoretic GSA provides an "outer loop" for accelerated product design by identifying the most and least sensitive input directions and performing subsequent optimization over appropriately reduced parameter subspaces.