将可解释的KAN网络与贝叶斯推断结合，实现科学计算中的可信不确定性量化。
Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
- 用稀疏变分高斯过程融合KAN结构，支持可扩展的贝叶斯推理。
- 在流体重构、多步预测和分布外检测中区分随机与认知不确定性。
- 适合需要可信预测的科学建模场景，如物理模拟与实验数据校准。
Kolmogorov-Arnold网络（KAN）作为传统多层感知机的可解释替代方案出现，但标准实现缺乏科学应用所需的严谨不确定性量化能力。本文提出一种框架，将稀疏变分高斯过程推断与KAN拓扑结合，实现样本量近线性复杂度的可扩展贝叶斯推断。通过解析矩匹配，将不确定性传播至深层加性结构，同时保持模型可解释性。三个案例研究验证了该方法区分随机不确定性与认知不确定性：流体流动重构中异方差测量噪声的校准、对流-扩散动力学多步预测中置信度下降的量化，以及卷积自编码器中的分布外检测。结果表明，稀疏变分高斯过程KAN（SVGP KAN）是科学机器学习中不确定性感知学习的有前景架构。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific applications. We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology, enabling scalable Bayesian inference with computational complexity quasi-linear in sample size. Through analytic moment matching, we propagate uncertainty through deep additive structures while maintaining interpretability. We use three example studies to demonstrate the framework's ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in fluid flow reconstruction, quantification of prediction confidence degradation in multi-step forecasting of advection-diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KANs) is a promising architecture for uncertainty-aware learning in scientific machine learning.
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