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

TL;DR

This work tackles UAV A2G channel modelling by introducing Physics-Inspired Kolmogorov–Arnol'd Networks (PIKAN), which fuse physics priors with the Kolmogorov–Arnol'd representation to yield interpretable symbolic activations while maintaining data-driven accuracy. By embedding elements such as free-space path loss and the two-ray model as inductive biases, PIKAN achieves competitive path-loss predictions with a compact parameter footprint (about $232$ parameters) and provides symbolic expressions that align with propagation physics. Through experiments on a UAV A2G rural dataset, PIKAN and its FSPL/Two-Ray variants outperform traditional deterministic baselines and approach the accuracy of deeper neural nets that use orders of magnitude more parameters, thereby offering a practical balance of interpretability, efficiency, and accuracy. The approach promises a scalable, explainable framework for UAV channel modelling relevant to beyond-5G and 6G networks.

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.

Figures (8)

• Figure 1: Training pipelines for Kolmogorov–Arnold Networks: (a) baseline pruning and symbolic refinement; (b) extended pipeline with physics-inspired symbolic fix.
• Figure 2: Grid search performance results: (a) training RMSE, (b) test RMSE, (c) test MAE, (d) test correlation scores.
• Figure 3: The base KAN structure before symbolification. The output node corresponds to the predicted path loss $L$ [dB], while the input nodes represent the selected significant features: center frequency $f_{\mathrm{c}}$, horizontal distance $d_{\mathrm{hor}}$, vertical distance $d_{\mathrm{ver}}$, and angles of arrival/departure $(\alpha_{\mathrm{AoA}}, \beta_{\mathrm{AoA}}, \alpha_{\mathrm{AoD}}, \beta_{\mathrm{AoD}})$.
• Figure 4: The pruned KAN structure after symbolification. Each node is associated with the best-fitting symbolic activation function chosen from the predefined library. Red color denotes the symbolic activation functions.
• Figure 5: The PIKAN structure inspired by free space path loss. Only functions related to distances and outer function are fixed. Red color denotes the symbolic activation functions.