Fourier neural networks as function approximators and differential equation solvers
Abstract 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.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 1829916
- Journal Information:
- Statistical Analysis and Data Mining, Journal Name: Statistical Analysis and Data Mining Journal Issue: 6 Vol. 14; ISSN 1932-1864
- Publisher:
- Wiley Blackwell (John Wiley & Sons)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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