Physics-Driven Learning of the Steady Navier-Stokes Equations Using Deep Convolutional Neural Networks
Year: 2022
Author: Hao Ma, Yuxuan Zhang, Nils Thuerey, Xiangyu Hu, Oskar J. Haidn
Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 715–736
Abstract
Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the physics-driven learning of complex flow fields with high resolutions. We propose the use of Convolutional neural networks (CNN) based U-net architectures to efficiently represent and reconstruct the input and output fields, respectively. By introducing Navier-Stokes equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents many of the difficulties associated with approaches employing fully connected neural networks. Several numerical experiments are conducted to investigate the behavior of the CNN approach, and the results indicate that a first-order accuracy has been achieved. Specifically for the case of a flow around a cylinder, different flow regimes can be learned and the adhered “twin-vortices” are predicted correctly. The numerical results also show that the training for multiple cases is accelerated significantly, especially for the difficult cases at low Reynolds numbers, and when limited reference solutions are used as supplementary learning targets.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0146
Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 715–736
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Deep learning physics-driven method convolutional neural networks Navier-Stokes equations.
Author Details
-
On the choice of physical constraints in artificial neural networks for predicting flow fields
Puri, Rishabh | Onishi, Junya | Rüttgers, Mario | Sarma, Rakesh | Tsubokura, Makoto | Lintermann, AndreasFuture Generation Computer Systems, Vol. 161 (2024), Iss. P.361
https://doi.org/10.1016/j.future.2024.07.009 [Citations: 0] -
Current and emerging deep-learning methods for the simulation of fluid dynamics
Lino, Mario | Fotiadis, Stathi | Bharath, Anil A. | Cantwell, Chris D.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 479 (2023), Iss. 2275
https://doi.org/10.1098/rspa.2023.0058 [Citations: 5] -
Assimilating experimental data of a mean three-dimensional separated flow using physics-informed neural networks
Steinfurth, B. | Weiss, J.Physics of Fluids, Vol. 36 (2024), Iss. 1
https://doi.org/10.1063/5.0183463 [Citations: 8] -
3D Super-Resolution Model for Vehicle Flow Field Enrichment
Trinh, Thanh Luan | Chen, Fangge | Nanri, Takuya | Akasaka, Kei2024 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), (2024), P.5814
https://doi.org/10.1109/WACV57701.2024.00572 [Citations: 0] -
Effect of network architecture on physics-informed deep learning of the Reynolds-averaged turbulent flow field around cylinders without training data
Harmening, Jan Hauke | Peitzmann, Franz-Josef | el Moctar, OuldFrontiers in Physics, Vol. 12 (2024), Iss.
https://doi.org/10.3389/fphy.2024.1385381 [Citations: 1] -
Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics
Lino, Mario | Fotiadis, Stathi | Bharath, Anil A. | Cantwell, Chris D.Physics of Fluids, Vol. 34 (2022), Iss. 8
https://doi.org/10.1063/5.0097679 [Citations: 34] -
Modeling of 3D Blood Flows with Physics-Informed Neural Networks: Comparison of Network Architectures
Moser, Philipp | Fenz, Wolfgang | Thumfart, Stefan | Ganitzer, Isabell | Giretzlehner, MichaelFluids, Vol. 8 (2023), Iss. 2 P.46
https://doi.org/10.3390/fluids8020046 [Citations: 12] -
Three-dimensional laminar flow using physics informed deep neural networks
Biswas, Saykat Kumar | Anand, N. K.Physics of Fluids, Vol. 35 (2023), Iss. 12
https://doi.org/10.1063/5.0180834 [Citations: 6] -
Combining Digital Twin and Machine Learning for the Fused Filament Fabrication Process
Butt, Javaid | Mohaghegh, VahajMetals, Vol. 13 (2022), Iss. 1 P.24
https://doi.org/10.3390/met13010024 [Citations: 8] -
Heat Conduction Plate Layout Optimization Using Physics-Driven Convolutional Neural Networks
Sun, Yang | Elhanashi, Abdussalam | Ma, Hao | Chiarelli, Mario RosarioApplied Sciences, Vol. 12 (2022), Iss. 21 P.10986
https://doi.org/10.3390/app122110986 [Citations: 2] -
Data-assisted training of a physics-informed neural network to predict the separated Reynolds-averaged turbulent flow field around an airfoil under variable angles of attack
Harmening, Jan Hauke | Pioch, Fabian | Fuhrig, Lennart | Peitzmann, Franz-Josef | Schramm, Dieter | el Moctar, OuldNeural Computing and Applications, Vol. 36 (2024), Iss. 25 P.15353
https://doi.org/10.1007/s00521-024-09883-9 [Citations: 1] -
A comprehensive deep learning geometric shape optimization framework with field prediction surrogate and reinforcement learning
Ma, Hao | Liu, Jianing | Ye, Mai | Haidn, Oskar J.Physics of Fluids, Vol. 36 (2024), Iss. 4
https://doi.org/10.1063/5.0198981 [Citations: 2]