GINNs: Graph-Informed Neural Networks for Multiscale Physics

Typically this requires casting the original deterministic physics-based model into a probabilistic framework where inputs or control variables (CVs) are treated as random variables with probability distributions derived from available experimental data, manufacturing constraints, design criteria, expert judgment, and/or other domain knowledge (e.g., see [1]). Running the physics-based model with CVs sampled according to these distributions yields corresponding realizations of the system response as characterized by quantities of interest (QoIs). Analysis of the uncertainty propagation from the CVs to the QoIs informs decision-making, e.g., it informs engineering decisions aimed at improving the quality and reliability of designed products and helps identify potential risks at early stages in the design and manufacturing process. Quantitatively assessing uncertainty propagation presents a fundamental challenge due to the computational cost of the underlying physics-based model. Even for a low number of CVs and QoIs, uncertainty quantification (UQ) for, e.g., accelerating the simulation-aided design of multiscale systems and data-centric engineering tasks more generally ([2]), requires a large number of repeated observations of QoIs to achieve a high degree of confidence in such an analysis. The sampling cost is further exacerbated in real-world applications where distributions on QoIs are typically non-Gaussian, skewed, and/or mutually correlated, and therefore need to be characterized by their full probability density function (PDF) rather than through summary statistics such as mean and variance. The computational cost of nonparametric methods to estimate these densities can become prohibitively high when using a fully-featured physics-based model to compute each sample. One approach to alleviate the computational burden is to derive a cheaper-to-compute surrogate for the physicsbased model's response enabling much faster generation of output data and thus overcoming computational bottlenecks.