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

arXiv: https://arxiv.org/abs/2510.06355 · HTML: https://mlsanity.com/paper/2510.06355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 6 of 6)

- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Accessing From The Sky: A Tutorial on UAV Communications for 5G and Beyond](https://mlsanity.com/paper/1903.05289/) (2019)
- [UAV Communications for 5G and Beyond: Recent Advances and Future Trends](https://mlsanity.com/paper/1901.06637/) (2019)
- [The choice of scaling technique matters for classification performance](https://mlsanity.com/paper/2212.12343/) (2022)
- [A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Data](https://mlsanity.com/paper/2406.14529/) (2024)
- [A Survey of Air-to-Ground Propagation Channel Modeling for Unmanned Aerial Vehicles](https://mlsanity.com/paper/1801.01656/) (2018)

## Abstract (arXiv)

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.