Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)

TL;DR

This paper introduces SVGP KAN, a scalable Bayesian framework combining Gaussian processes with Kolmogorov-Arnold Networks, enabling uncertainty quantification in scientific machine learning tasks while maintaining interpretability.

Contribution

It presents a novel integration of sparse variational Gaussian processes with Kolmogorov-Arnold Networks for scalable, uncertainty-aware scientific modeling.

Findings

Successfully distinguishes aleatoric and epistemic uncertainty.

Demonstrates improved uncertainty calibration in fluid flow reconstruction.

Effective out-of-distribution detection in autoencoders.

Abstract

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.