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.
Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KAN
Indian Institute of Technology, Delhi（印度理工学院德里分校）；Indian Institute of Technology, Dhanbad（印度理工学院丹巴德分校）；Sun Moon University（日月大学）；Amrita Vishwa Vidyapeetham（阿米塔大学）；United States DEVCOM Army Research Laboratory（美国DEVCOM陆军研究实验室）；University of Massachusetts at Boston（马萨诸塞大学波士顿分校）；Tulane University（杜兰大学）
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Brown University（布朗大学）；Division of Applied Mathematics, Brown University（布朗大学应用数学系）；School of Engineering, Brown University（布朗大学工程学院）；Center for Biomedical Engineering, Brown University（布朗大学生物医学工程中心）
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
Tsinghua University（清华大学）；Bauhaus-Universität Weimar（魏玛包豪斯大学）；CNPC Engineering Technology RD Company Limited（中国石油集团工程技术研究院有限公司）；Queensland University of Technology（昆士兰科技大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of North Carolina, Charlotte（北卡罗来纳大学夏洛特分校）；Delft University of Technology（代尔夫特理工大学）；University of Washington, Applied Mathematics（华盛顿大学应用数学系）；Brown University, Applied Mathematics（布朗大学应用数学系）
Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
School of Petroleum Engineering, Yangtze University（扬州大学石油工程学院）；School of Computer Science, Yangtze University（扬州大学计算机科学学院）；State Key Laboratory of Low Carbon Catalysis and Carbon Dioxide Utilization (Yangtze University)（扬州大学低碳催化与二氧化碳利用国家重点实验室）；Western Research Institute, Yangtze University（扬州大学西部研究院）
Optimized Architectures for Kolmogorov-Arnold Networks
Mathematics & Statistics, University of Vermont（佛蒙特大学数学与统计学系）；Vermont Complex Systems Center, University of Vermont（佛蒙特复杂系统中心）；Computer Science, University of Vermont（佛蒙特大学计算机科学系）
The Enhanced Physics-Informed Kolmogorov-Arnold Networks: Applications of Newton's Laws in Financial Deep Reinforcement Learning (RL) Algorithms
Virginia Polytechnic Institute（弗吉尼亚理工大学）；State University, Blacksburg, USA（州立大学，弗吉尼亚州黑斯堡）；Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam（胡志明银行大学，胡志明市）
Kolmogorov-Arnold networks for metal surface defect classification
AGH University of Krakow（克拉科夫AGH大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；University of Technology Sydney（悉尼科技大学）；Óbuda University（欧布达大学）；NASK National Research Institute（NASK国家研究院）
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学研究所）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University Berlin（柏林洪堡大学物理系）；Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究所）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学教育部量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
