KAN-GCN: Combining Kolmogorov-Arnold Network with Graph Convolution Network for an Accurate Ice Sheet Emulator

TL;DR

KAN-GCN integrates a Kolmogorov-Arnold Network front end with a Graph Convolution Network to create a fast, accurate ice-sheet emulator. The KAN provides feature-wise nonlinear encoding before spatial graph propagation, while residual one-step updates and feature-wise loss weighting improve training stability and calibration. Across Pine Island Glacier simulations on multiple mesh sizes, KAN-GCN generally surpasses pure GCN and MLP-GCN baselines, especially for velocity, with favorable accuracy-throughput trade-offs on coarser meshes. This approach enables efficient large transient scenario sweeps, offering practical benefits for sea-level rise forecasting.

Abstract

We introduce KAN-GCN, a fast and accurate emulator for ice sheet modeling that places a Kolmogorov-Arnold Network (KAN) as a feature-wise calibrator before graph convolution networks (GCNs). The KAN front end applies learnable one-dimensional warps and a linear mixing step, improving feature conditioning and nonlinear encoding without increasing message-passing depth. We employ this architecture to improve the performance of emulators for numerical ice sheet models. Our emulator is trained and tested using 36 melting-rate simulations with 3 mesh-size settings for Pine Island Glacier, Antarctica. Across 2- to 5-layer architectures, KAN-GCN matches or exceeds the accuracy of pure GCN and MLP-GCN baselines. Despite a small parameter overhead, KAN-GCN improves inference throughput on coarser meshes by replacing one edge-wise message-passing layer with a node-wise transform; only the finest mesh shows a modest cost. Overall, KAN-first designs offer a favorable accuracy vs. efficiency trade-off for large transient scenario sweeps.

Figures (1)

• Figure 1: Schematic illustration of our proposed KAN-GCN emulator.