  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.
