Uncertainty-Aware Flow Field Reconstruction Using SVGP Kolmogorov-Arnold Networks

TL;DR

This paper presents a novel machine learning framework using sparse variational Gaussian processes within Kolmogorov-Arnold networks for uncertainty-aware reconstruction of flow fields from sparse measurements, outperforming classical methods in uncertainty calibration.

Contribution

The paper introduces SVGP-KAN, a new approach that extends classical flow reconstruction methods with principled uncertainty quantification and systematic comparison with existing techniques.

Findings

Achieves comparable accuracy to classical methods

Provides well-calibrated uncertainty estimates

Effective across low sampling rates (0.5% to 10%)

Abstract

Reconstructing time-resolved flow fields from temporally sparse velocimetry measurements is critical for characterizing many complex thermal-fluid systems. We introduce a machine learning framework for uncertainty-aware flow reconstruction using sparse variational Gaussian processes in the Kolmogorov-Arnold network topology (SVGP-KAN). This approach extends the classical foundations of Linear Stochastic Estimation (LSE) and Spectral Analysis Modal Methods (SAMM) while enabling principled epistemic uncertainty quantification. We perform a systematic comparison of our framework with the classical reconstruction methods as well as Kalman filtering. Using synthetic data from pulsed impingement jet flows, we assess performance across fractional PIV sampling rates ranging from 0.5% to 10%. Evaluation metrics include reconstruction error, generalization gap, structure preservation, and uncertainty calibration. Our SVGP-KAN methods achieve reconstruction accuracy comparable to established methods, while also providing well-calibrated uncertainty estimates that reliably indicate when and where predictions degrade. The results demonstrate a robust, data-driven framework for flow field reconstruction with meaningful uncertainty quantification and offer practical guidance for experimental design in periodic flows.