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

2025-10-28

AI Summary

High computational cost and the trade-off between accuracy and efficiency hinder large-scale ice-sheet numerical simulations. To address this, we propose KAN-first, a novel graph neural network (GNN) surrogate model that integrates a learnable Kolmogorov–Arnold Network (KAN) as a node-wise 1D nonlinear feature calibration module prior to graph convolutional layers. This design enhances input representation capacity while replacing part of the message-passing computation, thereby reducing overhead and improving inference throughput—especially on coarse grids. Evaluated on 36 transient melt-rate scenarios from Antarctica’s Pine Island Glacier, KAN-first achieves superior accuracy over baseline GCN and MLP-GCN models across 2–5 layer configurations, with negligible parameter overhead. The approach significantly improves the accuracy–efficiency Pareto frontier, establishing a new paradigm for high-fidelity, computationally efficient surrogate modeling of ice-sheet dynamics.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• Accurately emulating ice sheet dynamics using neural networks
• Improving feature conditioning without increasing message-passing depth
• Balancing computational efficiency with accuracy in glacier modeling

Innovation

• KAN-GCN integrates Kolmogorov-Arnold Network with GCN
• KAN applies learnable warps and linear mixing step
• Replaces message-passing layer with node-wise transform for efficiency