GINNs: Graph-Informed Neural Networks for Multiscale Physics

TL;DR

GINNs combine deep learning with probabilistic graphical models to efficiently simulate multiscale physics systems, reducing computational costs and improving probability distribution estimates of key quantities.

Contribution

This paper introduces GINNs, a novel hybrid framework that integrates PGMs with neural networks to enhance physics-based modeling and prediction in complex systems.

Findings

GINNs accurately estimate non-Gaussian QoIs with tight confidence intervals.

The approach significantly reduces computational costs compared to traditional physics simulations.

Demonstrated effectiveness in a supercapacitor energy storage application.

Abstract

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.