Fourier Neural Networks as Function Approximators and Differential\n Equation Solvers

2020/05/26 by Marième Ngom, Ngom, Marieme, Oana Marin +1
Physics and Astronomy · Computer Science · Materials Science · #Model Reduction and Neural Networks #Neural Networks and Applications #Magnetic Properties and Applications

paper · pdf · doi:10.48550/arxiv.2005.13100

Abstract

We present a Fourier neural network (FNN) that can be mapped directly to the\nFourier decomposition. The choice of activation and loss function yields\nresults that replicate a Fourier series expansion closely while preserving a\nstraightforward architecture with a single hidden layer. The simplicity of this\nnetwork architecture facilitates the integration with any other\nhigher-complexity networks, at a data pre- or postprocessing stage. We validate\nthis FNN on naturally periodic smooth functions and on piecewise continuous\nperiodic functions. We showcase the use of this FNN for modeling or solving\npartial differential equations with periodic boundary conditions. The main\nadvantages of the current approach are the validity of the solution outside the\ntraining region, interpretability of the trained model, and simplicity of use.\n

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