Graph convolutional network as a fast statistical emulator for numerical ice sheet modeling

TL;DR

This study tackles the CPU bottleneck of ISSM-based ice-sheet modeling by proposing a GCN emulator that operates on ISSM's unstructured meshes. The GCN is trained on 20-year Pine Island Glacier simulations across multiple mesh resolutions and basal-melting scenarios and benchmarked against CNN and MLP baselines. Results show the GCN reproduces ice thickness with RMSE ≈ 12 m and ice velocity with RMSE in the tens of m/year range, with $R \approx 0.998$–$0.999$, and achieves GPU speed-ups of roughly 60–100× over ISSM. The work demonstrates that graph-based emulation can capture fine-resolution dynamics in irregular meshes and enables rapid sensitivity analyses of basal melting and other climate forcings, with potential extensions to physics-informed and dynamic-graph models.

Abstract

The Ice-sheet and Sea-level System Model (ISSM) provides numerical solutions for ice sheet dynamics using finite element and fine mesh adaption. However, considering ISSM is compatible only with central processing units (CPUs), it has limitations in economizing computational time to explore the linkage between climate forcings and ice dynamics. Although several deep learning emulators using graphic processing units (GPUs) have been proposed to accelerate ice sheet modeling, most of them rely on convolutional neural networks (CNNs) designed for regular grids. Since they are not appropriate for the irregular meshes of ISSM, we use a graph convolutional network (GCN) to replicate the adapted mesh structures of the ISSM. When applied to transient simulations of the Pine Island Glacier (PIG), Antarctica, the GCN successfully reproduces ice thickness and velocity with a correlation coefficient of approximately 0.997, outperforming non-graph models, including fully convolutional network (FCN) and multi-layer perceptron (MLP). Compared to the fixed-resolution approach of the FCN, the flexible-resolution structure of the GCN accurately captures detailed ice dynamics in fast-ice regions. By leveraging 60-100 times faster computational time of the GPU-based GCN emulator, we efficiently examine the impacts of basal melting rates on the ice sheet dynamics in the PIG.

Figures (10)

• Figure 1: (a) Location of Pine Island Glacier (PIG) in the Antarctic indicated by a red poylgon. Dashed lines are 10-degree-apart latitudes and 30-degree-apart longitudes. (b) Initial ice velocity, (b) surface elevation, and (c) ice thickness of the PIG. The meshes in (b), (c), and (d) are initialized with 20 km mesh size. The extent of meshes in (b), (c), and (d) correspond to the red polygon in (a).
• Figure 2: Structures of data and node connectivity for different deep learning architectures: graph convolutional network (GCN), convolutional neural network (CNN), and multi-layer perceptron (MLP) for fast and slow ice conditions. The graph structure of GCN is converted from the finite element (i.e., unstructured meshes) of ISSM: the fast-ice area has a fine mesh resolution (a), and the slow-ice area has a coarse mesh resolution (d), and the nodes of the element are connected as edges. The graph convolution of a node is determined by the neighboring nodes. The regular grid structure of CNN has the same resolution (2 km) for all locations regardless of ice velocity (b and e), and the convolutional kernel size is fixed to 3$\times$3 for all locations. The node of MLP is the same as the node of ISSM and GCN, but the connectivity between nodes is not used; only the features of a node are used to predict the ice condition at that node (c and f).
• Figure 3: Schematic illustration of the graph convolutional network (GCN) emulator.
• Figure 4: RMSE of ice thickness by years for different basal melting rates ($r$) and initial mesh sizes ($M_0$).
• Figure 5: Maps of ice thickness modeled by the ISSM simulation and difference with deep learning emulators (GCN, FCN, and MLP from top to bottom) for two different basal melting rates ($r$=10 and 70 m $\text{a}^{-1}$) and different initial mesh sizes ($M_0$=2, 5, and 10 km). Each map shows the 20-year average of ice thickness. The ice thickness maps for years 1, 10, and 20 are shown in Figure \ref{['A1']}. The dashed grids indicate a Cartesian 20 km grid, and the magenta line indicates the grounding line. The south side of the grounding line is floating, and the north side of the grounding line is grounded.