A Primer on Kolmogorov-Arnold Networks (KANs) for Probabilistic Time Series Forecasting

TL;DR

This work addresses uncertainty-aware time-series forecasting for satellite resource allocation by introducing Probabilistic Kolmogorov-Arnold Networks (P-KANs), which replace scalar weights with spline-based functional connections and directly parameterize predictive distributions. By evaluating Gaussian and Student-$t$ likelihoods on GEO satellite traffic data, the authors demonstrate that P-KANs deliver superior calibration and accuracy while using substantially fewer parameters than MLP baselines. The framework enables dynamic thresholding via high-quantile forecasts (e.g., $P_{99}$), improving efficiency and reliability in resource provisioning. The findings show that Gaussian P-KANs offer robust, conservative forecasts suitable for safety-critical contexts, whereas Student-$t$ P-KANs provide sharper distributions that boost efficiency under stable demand, making P-KAN a practical tool for uncertainty-aware forecasting in satellite communications and other resource-constrained domains.

Abstract

This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and directly parameterizing predictive distributions, P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics. We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation. Results show that P-KANs consistently outperform Multi Layer Perceptron (MLP) baselines in both accuracy and calibration, achieving superior efficiency-risk trade-offs while using significantly fewer parameters. We build up P-KANs on two distributions, namely Gaussian and Student-t distributions. The Gaussian variant provides robust, conservative forecasts suitable for safety-critical scenarios, whereas the Student-t variant yields sharper distributions that improve efficiency under stable demand. These findings establish P-KANs as a powerful framework for probabilistic forecasting with direct applicability to satellite communications and other resource-constrained domains.

Figures (5)

• Figure 1: Forecasts over one satellite beam using P-KAN showing predictive intervals and adaptive thresholding (a) under Gaussian likelihood (b) under Student-$t$ likelihood.
• Figure 2: FIC at the 10%, 50% and 90% nominal levels for probabilistic models.
• Figure 3: Breakdown of resource allocation efficiency and risk across models, showing the proportion of PRB savings, overprovisioning and underprovisioning.
• Figure 4: Pareto analysis of PRB savings versus underprovisioning.
• Figure 5: Trainable parameters across probabilistic and PF models.