Fourier Neural Networks as Function Approximators and Differential Equation Solvers
Argonne National Laboratory（阿贡国家实验室）
Marieme Ngom, Oana Marin
备注：
22 pages, 10 figures Added figures to explain the initialization strategy, fixed typos, updated abstract and modified title to make it more self explanatory
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.
Peking University（北京大学）；Shanghai Jiao Tong University（上海交通大学）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）
Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis
1 Max-Planck-Institute for Plasma Physics, 17491 Greifswald, Germany 2 Institute for Research in Electronics \& Applied Physics, University of Maryland, MD 20742, USA 3 Mechanical；Aerospace Engineering, Princeton University, NJ 08544, USA
FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation
Department of AI, Chung-Ang University（人工智能学院， Chung-Ang 大学）；Department of Mathematics, Pohang University of Science and Technology (POSTECH)（数学系， Pohang 大学 of Science and Technology (POSTECH)）
Hankel-FNO: Fast Underwater Acoustic Charting Via Physics-Encoded Fourier Neural Operator
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China（信息科学与电子工程学院，浙江大学，杭州，中国）；Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093, USA（Scripps 海洋研究所，加州大学圣地亚哥分校，La Jolla，加利福尼亚州 92093，美国）
King Abdullah University of Science and Technology (KAUST)（沙特阿拉伯国王 Abdullah 科技大学(KAUST)（注：此处“King Abdullah University of Science and Technology”的中文常见译名为“沙特国王 Abdullah 科技大学”，但根据原文本括号内缩写“KAUST”，保留“国王 Abdullah 科技大学(KAUST)”或更简洁的“沙特国王 Abdullah 科技大学”均可，此处按原文括号内缩写整合为“沙特阿拉伯国王 Abdullah 科技大学(KAUST)”以确保准确对应））
Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology
Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Cardiovascular Institute, Stanford University（斯坦福大学心血管研究所）；Pediatric Cardiology, Stanford University（斯坦福大学儿科心脏病研究所）；Department of Bioengineering, Stanford University（斯坦福大学生物工程系）
