PIKAN: Physics-Inspired Kolmogorov-Arnold Networks for Explainable UAV Channel Modelling

2025-10-07

AI Summary

Addressing the challenge of balancing accuracy and interpretability in unmanned aerial vehicle (UAV) air-to-ground (A2G) channel modeling—particularly under non-stationary propagation conditions—this paper proposes a physics-guided, lightweight, and interpretable neural network. The method innovatively incorporates physical priors—such as free-space path loss and two-ray reflection—into a Kolmogorov–Arnold network architecture as flexible inductive biases, enabling parameter-efficient learning while preserving symbolic interpretability. Unlike conventional physics-informed neural networks (PINNs), it offers enhanced adaptability to dynamic environments. Evaluated on real UAV channel measurements, the model achieves accuracy comparable to deep learning baselines using only 232 parameters—37× fewer than typical deep models—and directly outputs closed-form analytical expressions consistent with electromagnetic wave propagation principles.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Unmanned aerial vehicle (UAV) communications demand accurate yet interpretable air-to-ground (A2G) channel models that can adapt to nonstationary propagation environments. While deterministic models offer interpretability and deep learning (DL) models provide accuracy, both approaches suffer from either rigidity or a lack of explainability. To bridge this gap, we propose the Physics-Inspired Kolmogorov-Arnold Network (PIKAN) that embeds physical principles (e.g., free-space path loss, two-ray reflections) into the learning process. Unlike physics-informed neural networks (PINNs), PIKAN is more flexible for applying physical information because it introduces them as flexible inductive biases. Thus, it enables a more flexible training process. Experiments on UAV A2G measurement data show that PIKAN achieves comparable accuracy to DL models while providing symbolic and explainable expressions aligned with propagation laws. Remarkably, PIKAN achieves this performance with only 232 parameters, making it up to 37 times lighter than multilayer perceptron (MLP) baselines with thousands of parameters, without sacrificing correlation with measurements and also providing symbolic expressions. These results highlight PIKAN as an efficient, interpretable, and scalable solution for UAV channel modelling in beyond-5G and 6G networks.

Problem

• Develops interpretable UAV channel models for nonstationary environments
• Integrates physical principles into neural networks for explainability
• Creates lightweight models with symbolic expressions matching propagation laws

Innovation

• Embeds physical principles into learning process
• Introduces flexible inductive biases for training
• Achieves accuracy with lightweight symbolic expressions