  Although the finite element approach of the Ice-sheet and Sea-level System
Model (ISSM) solves ice dynamics problems governed by Stokes equations quickly
and accurately, such numerical modeling requires intensive computation on
central processing units (CPU). In this study, we develop graph neural networks
(GNN) as fast surrogate models to preserve the finite element structure of
ISSM. Using the 20-year transient simulations in the Pine Island Glacier (PIG),
we train and test three GNNs: graph convolutional network (GCN), graph
attention network (GAT), and equivariant graph convolutional network (EGCN).
These GNNs reproduce ice thickness and velocity with better accuracy than the
classic convolutional neural network (CNN) and multi-layer perception (MLP). In
particular, GNNs successfully capture the ice mass loss and acceleration
induced by higher basal melting rates in the PIG. When our GNN emulators are
implemented on graphic processing units (GPUs), they show up to 50 times faster
computational time than the CPU-based ISSM simulation.
