Mutual Information for Explainable Deep Learning of Multiscale Systems
This work addresses the need for explainable deep learning in multiscale systems, such as consumer electronics and hypersonic vehicles, by providing a method to identify sensitive input directions for optimization, though it is incremental as it builds on existing information-theoretic approaches.
The paper tackles the challenge of rapid simulation-based prototyping for complex systems by developing a model-agnostic global sensitivity analysis using differential mutual information to rank the effects of control variables on quantities of interest, and demonstrates its utility on energy storage applications to accelerate product design.
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.