Uncertainty quantification for scientific machine learning using sparse variational Gaussian process Kolmogorov–Arnold networks (SVGP KAN)

Abstract Kolmogorov–Arnold networks (KANs) 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 (SVGP) inference with the Kolmogorov–Arnold topology, enabling scalable Bayesian inference with computational complexity that is in theory 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 examine the framework’s ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in scalar field prediction, quantification of prediction confidence degradation in multi-step forecasting of advection–diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest SVGP-KANs as a promising architecture for uncertainty-aware learning in scientific machine learning.