Residual Factorized Fourier Neural Operator for simulation of three-dimensional turbulence

Maximilian Dauner, Ankith Bheemanakone, Benedikt Zönnchen, Gudrun Socher

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: factorized fourier neural operator, fourier neural operator, navier stokes, three-dimensional turbulence prediction

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TL;DR: A Factorized Fourier Neural Operator based approach for the three-dimensional turbulence prediction around a cube.

Abstract:

Neural Operators, particularly Fourier Neural Operators (FNO), have proven highly effective in simulating partial differential equations (PDEs), such as the Navier-Stokes equations. We propose the Residual Factorized Fourier Neural Operator (Res-F-FNO) for simulating three-dimensional (3D) flows, specifically focusing on flow dynamics around a cube. We extend the Factorized Fourier Neural Operator (F-FNO) architecture by incorporating additional residual connections. This change effectively reintroduces small-scale dynamic flows that may be lost due to truncated Fourier modes, resulting in improved accuracy when modeling wind fields. Our proposed Res-F-FNO model surpasses the performance of the standard F-FNO, achieving an error reduction of over 30% in simulating 3D flows. Furthermore, we propose the concept of a skip-corrector, to address the problem of accumulated errors over multiple time steps. The skip-corrector was specifically trained to predict the behaviour of turbulences at a considerably extended time interval. Incorporating the skip-corrector into the prediction process reduces the average error in simulating 100 time steps by more than 50%. Additionally, we adopt a modified training approach in which random time steps are chosen as the initial condition for each sample in every epoch, as opposed to generating a dataset by propagating each sample across all time steps. This leads to a significant reduction in the the number of training iterations required for the models to achieve convergence.

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Submission Number: 9242