Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
This addresses the need for interpretable and uncertainty-aware models in scientific machine learning, though it is an incremental improvement by combining existing methods.
The paper tackled the lack of principled uncertainty quantification in Kolmogorov-Arnold Networks by integrating sparse variational Gaussian process inference, enabling scalable Bayesian inference with quasi-linear computational complexity. It demonstrated the framework's ability to distinguish aleatoric from epistemic uncertainty in applications like fluid flow reconstruction and advection-diffusion forecasting.
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.