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

TL;DR

KAN-GCN is a novel ice sheet emulator combining Kolmogorov-Arnold Networks with graph convolutional networks, enhancing accuracy and efficiency in modeling melting rates across different mesh resolutions.

Contribution

The paper introduces KAN-GCN, a new architecture that improves ice sheet modeling accuracy and inference speed by integrating a Kolmogorov-Arnold Network as a feature calibrator before GCNs.

Findings

KAN-GCN matches or exceeds baseline accuracy.

Improves inference throughput on coarser meshes.

Maintains modest computational cost at fine mesh resolution.

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.