A surrogate neural network method for restoring the flow field from a homogeneous field by iterations in calculations of steady turbulent flows

Petrov M.N., Zimina S.V.
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In recent years, the use of neural network models for solving aerodynamics problems has become widespread. These models, trained on a set of previously obtained solutions, predict solutions to new problems. They are, in essence, interpolation algorithms. An alternative approach is to construct a neural network operator. This is a neural network that reproduces a numerical method used to solve a problem. It allows to find the solution in iterations. The paper considers the construction of such an operator using the UNet neural network with a spatial attention mechanism. It solves flow problems on a rectangular uniform grid that is common to a streamlined body and flow field. A correction mechanism is proposed to clarify the obtained solution. The problem of the stability of such an algorithm for solving a stationary problem is analyzed, and a comparison is made with other variants of its construction, including pushforward trick and positional encoding. The issue of selecting a set of iterations for forming a train dataset is considered, and the behavior of the solution is assessed using repeated use of a neural network operator.

A demonstration of the method is provided for the case of flow around a rounded plate with a turbulent flow, with various options for rounding, for fixed parameters of the incoming flow, with Reynolds number $\text{Re} = 10^5$ and Mach number $M = 0.15$. Since flows with these parameters of the incoming flow can be considered incompressible, only velocity components are directly studied. At the same time, the neural network model used to construct the operator has a common decoder for both velocity components. Comparison of flow fields and velocity profiles along the normal and outline of the body, obtained using a neural network operator and numerical methods, is carried out. Analysis is performed both on the plate and rounding. Simulation results confirm that the neural network operator allows finding a solution with high accuracy and stability.

Keywords: aerodynamics, turbulence, neural operator, convolutional neural network, UNet, attention
Citation in English: Petrov M.N., Zimina S.V. A surrogate neural network method for restoring the flow field from a homogeneous field by iterations in calculations of steady turbulent flows // Computer Research and Modeling, 2025, vol. 17, no. 2, pp. 179-197
Citation in English: Petrov M.N., Zimina S.V. A surrogate neural network method for restoring the flow field from a homogeneous field by iterations in calculations of steady turbulent flows // Computer Research and Modeling, 2025, vol. 17, no. 2, pp. 179-197
DOI: 10.20537/2076-7633-2025-17-2-179-197
URL: http://crm-en.ics.org.ru/journal/article/3593/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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