GINNs: Graph-Informed Neural Networks for Multiscale Physics
This addresses the problem of high computational costs in simulation-based decision-making for multiscale physics, offering a hybrid method that is incremental in combining existing techniques.
The paper tackles the challenge of accelerating predictions for multiscale physics systems by introducing Graph-Informed Neural Networks (GINNs), which combine deep learning with probabilistic graphical models to act as surrogates for expensive physics-based models, demonstrating in a supercapacitor energy storage application that they produce kernel density estimates with tight confidence intervals.
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and multiphysics systems. GINNs address the twin challenges of removing intrinsic computational bottlenecks in physics-based models and generating large data sets for estimating probability distributions of quantities of interest (QoIs) with a high degree of confidence. Both the selection of the complex physics learned by the NN and its supervised learning/prediction are informed by the PGM, which includes the formulation of structured priors for tunable control variables (CVs) to account for their mutual correlations and ensure physically sound CV and QoI distributions. GINNs accelerate the prediction of QoIs essential for simulation-based decision-making where generating sufficient sample data using physics-based models alone is often prohibitively expensive. Using a real-world application grounded in supercapacitor-based energy storage, we describe the construction of GINNs from a Bayesian network-embedded homogenized model for supercapacitor dynamics, and demonstrate their ability to produce kernel density estimates of relevant non-Gaussian, skewed QoIs with tight confidence intervals.