Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop a physics-inspired graph neural network (GNN) surrogate that operates directly on unstructured meshes and leverages the flexibility of graph attention. To improve both training efficiency and generalization properties of the model, we introduce a domain decomposition (DD) strategy that partitions the mesh into subdomains, trains local GNN surrogates in parallel, and aggregates their predictions. We then employ transfer learning to fine-tune models across subdomains, accelerating training and improving accuracy in data-limited settings. Applied to ice sheet simulations, our approach accurately predicts full-field velocities on high-resolution meshes, substantially reduces training time relative to training a single global surrogate model, and provides a ripe foundation for UQ objectives. Our results demonstrate that graph-based DD, combined with transfer learning, provides a scalable and reliable pathway for training GNN surrogates on massive PDE-governed systems, with broad potential for application beyond ice sheet dynamics.

In this article, the utility of graph neural network (GNN) surrogates for Monte Carlo (MC) sampling-based risk quantification in daily operations of power grid is investigated. The MC simulation process necessitates solving a large number of optimal power flow (OPF) problems corresponding to the sample values of stochastic grid variables (power demand and renewable generation), which is computationally prohibitive. Computationally inexpensive surrogates of the OPF problem provide an attractive alternative for expedited MC simulation. GNN surrogates are especially suitable due to their superior ability to handle graph-structured data. Therefore, GNN surrogates of OPF problem are trained using supervised learning. They are then used to obtain Monte Carlo (MC) samples of the quantities of interest (operating reserve, transmission line flow) given the (hours-ahead) probabilistic wind generation and load forecast. The utility of GNN surrogates is evaluated by comparing OPF-based and GNN-based grid reliability and risk for IEEE Case118 synthetic grid. It is shown that the GNN surrogates are sufficiently accurate for predicting the (bus-level, branch-level and system-level) grid state and enable fast as well as accurate operational risk quantification for power grids. The article thus develops various tools for fast reliability and risk quantification for real-world power grids using GNNs.