Application of Graph Neural Network Architectures for Approximating Solutions to Navier-Stokes Equations in Three-Dimensional Cases

Аuthors

Fedorov A. S.^*, Kondarattsev V. L.^**, Koval' M. R.^***, Popov A. V.^****, Gulyaev A. N.^*****

Bauman Moscow State Technical University, Moscow, Russian Federation

*e-mail: fedorov.a.s@bmstu.ru
**e-mail: vlkondarattsev@bmstu.ru
***e-mail: koval.m@bmstu.ru
****e-mail: popov.a@bmstu.ru
*****e-mail: gulyaev.a@bmstu.ru

Abstract

The objective of this work is to develop neural network approaches capable of approximating steady-state solutions to the Navier-Stokes equations in three-dimensional cases for both compressible and incompressible flows. This objective emerged from two sources: firstly, from a project aimed at developing a software-methodological framework for supercomputing multiphysics simulation of dynamic processes involving UAVs deployed from carrier aircraft (a contemporary technological concept for long-range UAV delivery for mission execution), and secondly, as part of exploratory research into the applicability of machine learning methods in CFD problems.
This paper proposes two architectures based on graph convolution operators. The first architecture consists of an encoder-decoder framework where the latent feature space serves as a phase vector; however, this architecture is applicable only to two-dimensional cases. The second architecture, designed for three-dimensional cases, represents a hybrid solver: initial approximation and final closure are achieved through the application of the HiSA solver for fields defined on finite volume meshes, while the solver iterations between these two processes are approximated by a deep graph convolutional neural network.
In addition to the architectures, techniques for validation and verification of the developed models are proposed, and a training dataset has been developed consisting of a collection of solutions computed using numerical methods for problems in both two-dimensional and three-dimensional cases for various bodies and different flow regimes. Additionally, results are presented on the implementation approach for working with graph convolution operators on computational systems with distributed GPU architectures.

Keywords:

Navier-Stokes equations; deep learning; training dataset; aerodynamic characteristics; aerodynamics; graph neural networks; encoder-decoder; CFD; finite volume method; supercomputing simulation

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