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.

翻译：无人机通信需要准确且可解释的空对地信道模型，并能适应非平稳的传播环境。确定性模型具有可解释性，深度学习模型则提供高精度，但两种方法均存在僵化或缺乏可解释性的问题。为弥补这一差距，我们提出物理启发式Kolmogorov-Arnold网络，其将物理原理（如自由空间路径损耗、双射线反射）嵌入学习过程。与物理信息神经网络不同，PIKAN通过将物理信息作为灵活的归纳偏置引入，从而在应用物理信息时更具灵活性，实现了更灵活的训练过程。基于无人机空对地实测数据的实验表明，PIKAN在达到与深度学习模型相当精度的同时，能提供符合传播规律的符号化可解释表达式。值得注意的是，PIKAN仅用232个参数即实现此性能，相比具有数千参数的多层感知机基线模型轻量高达37倍，且在保持与实测数据相关性的同时提供符号化表达式。这些结果凸显了PIKAN作为面向5G-Advanced及6G网络的高效、可解释、可扩展的无人机信道建模解决方案的潜力。