用KAN优化图卷积，提升冰盖模拟器精度与速度
KAN-GCN: Combining Kolmogorov-Arnold Network with Graph Convolution Network for an Accurate Ice Sheet Emulator
- KAN前置校准特征，替代部分图卷积层，增强非线性表达
- 在36次模拟、3种网格下，2-5层架构均优于或持平基线模型
- 适合大规模冰盖演化模拟，尤其在粗网格下推理更快
我们提出KAN-GCN，一种用于冰盖建模的快速高精度模拟器。该模型将科尔莫戈罗夫-阿诺德网络（KAN）置于图卷积网络（GCN）之前，作为特征校准器。KAN通过可学习的一维变形和线性混合步骤，提升特征条件化与非线性编码能力，且不增加消息传递深度。我们在南极皮恩岛冰川的36次融化率模拟中训练并测试该模型，涵盖3种网格尺寸。在2至5层架构中，KAN-GCN在精度上匹配或超过纯GCN和MLP-GCN基线。尽管参数略有增加，但其在粗网格下通过用节点级变换替代一层边级消息传递，显著提升推理吞吐量；仅在最细网格下有小幅开销。总体而言，先KAN后GCN的设计在大范围瞬态情景模拟中提供了更优的精度与效率权衡。
原文摘要 · Abstract (English)
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.
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