Fourier neural networks as function approximators and differential equation solvers

Statistical Analysis and Data Mining

article

Marieme Ngom¹  Oana Marin¹ 

[1] Mathematics and Computer Science Division, Argonne National Laboratory

关键词: differential equations;    Fourier decomposition;    neural networks;   

DOI  :  10.1002/sam.11531

学科分类：社会科学、人文和艺术（综合）

来源: John Wiley & Sons, Inc.

【 摘 要 】

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.

【 授权许可】

Unknown