Fourier Neural Operator Network for Efficiently Approximating Non-uniform Steady Laminar Flow Solutions Around Obstacles

Abstract

Abstract Fluid flow exhibits strong nonlinearity, and traditional solutions based on computational fluid dynamics (CFD) are limited by high computational costs. To efficiently model complex fluid dynamics, this study proposes a Fourier neural operator network (FNONet) to approximate solutions for 2D incompressible non-uniform steady laminar flows around obstacles. FNONet transforms flow geometry into Fourier space via discrete Fourier transform (DFT), parameterizes integral kernels using a neural network, and reconstructs velocity and pressure fields through hybrid frequency-spatial computations. A pressure gradient-constrained data-driven loss function is introduced to incorporate spatial-domain errors and frequency-domain pressure gradient constraints, thereby enhancing prediction accuracy near fluid-solid interfaces. Experiments demonstrate that the total mean squared error (MSE) of FNONet is over 20 times lower than that of convolutional neural network (CNN) based framework and 1.5 times lower than that of CNN-Transformer based framework. Compared with traditional CFD solvers, FNONet achieves a prediction speedup of over 3 orders of magnitude on central processing units (CPUs) and 4 orders of magnitude on graphics processing units (GPUs). The robustness and generalization of the model to unseen geometries are validated through qualitative visual analysis and quantitative error metrics on test datasets, providing a promising data-driven approach for CFD.

Affiliated Institutions

• Mongolian University of Science and Technology MN

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