This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and directly parameterizing predictive distributions, P-KANs offer expressive yet parameter-efficient models capable of capturing nonlinear and heavy-tailed dynamics. We evaluate P-KANs on satellite traffic forecasting, where uncertainty-aware predictions enable dynamic thresholding for resource allocation. Results show that P-KANs consistently outperform Multi Layer Perceptron (MLP) baselines in both accuracy and calibration, achieving superior efficiency-risk trade-offs while using significantly fewer parameters. We build up P-KANs on two distributions, namely Gaussian and Student-t distributions. The Gaussian variant provides robust, conservative forecasts suitable for safety-critical scenarios, whereas the Student-t variant yields sharper distributions that improve efficiency under stable demand. These findings establish P-KANs as a powerful framework for probabilistic forecasting with direct applicability to satellite communications and other resource-constrained domains.
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）
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）
DAE-KAN: A Kolmogorov-Arnold Network Model for High-Index Differential-Algebraic Equations
School of Computer Science and Cyber Engineering, Guangzhou University（广州大学计算机科学与网络工程学院）；Huangpu Research School of Guangzhou University（广州大学黄埔研究学院）；Department of Mathematics, Morgan State University（摩根州立大学数学系）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（高性能计算研究所（IHPC），科技研究局（A*STAR））；Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR)（前沿人工智能研究中心（CFAR），科技研究局（A*STAR））
Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting
School of Information Science and Engineering, Southeast University（信息科学与工程学院，东南大学）；School of Economics and Management, Southeast University（经济管理学院，东南大学）
Scientific Machine Learning with Kolmogorov-Arnold Networks
Energy \& Intelligence Lab, Department of Chemical Engineering, University of Utah, Salt Lake City, Utah 84112, USA；Department of Mechanical Engineering, School of Engineering, Urmia University of Technology, Urmia, Iran
Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning
Energy \& Intelligence Lab, Department of Chemical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, School of Engineering, Urmia University of Technology, Urmia, Iran
Massachusetts Institute of Technology（麻省理工学院）；The NSF Institute for Artificial Intelligence and Fundamental Interactions（NSF人工智能与基本相互作用研究所）；California Institute of Technology（加州理工学院）
Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
Indian Institute of Science Education and Research Mohali（印度科学教育与研究研究所莫哈利分校）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究研究所蒂鲁文南特布勒姆分校）
Multilevel Training for Kolmogorov Arnold Networks
Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论 division）；Center for Computing Research, Sandia National Laboratories（桑迪亚国家实验室计算研究中心）
Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
Department of Materials Science and Engineering, Delft University of Technology（材料科学与工程系，代尔夫特理工大学）；Department of Biomechanical Engineering, Delft University of Technology（生物机械工程系，代尔夫特理工大学）
