Volume 56, pp. 235-255, 2022.

Surrogate convolutional neural network models for steady computational fluid dynamics simulations

Matthias Eichinger, Alexander Heinlein, and Axel Klawonn

Abstract

A convolution neural network (CNN)-based approach for the construction of reduced order surrogate models for computational fluid dynamics (CFD) simulations is introduced; it is inspired by the approach of Guo, Li, and Iori [X. Guo, W. Li, and F. Iorio, Convolutional neural networks for steady flow approximation, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '16, New York, USA, 2016, ACM, pp. 481–490]. In particular, the neural networks are trained in order to predict images of the flow field in a channel with varying obstacle based on an image of the geometry of the channel. A classical CNN with bottleneck structure and a U-Net are compared while varying the input format, the number of decoder paths, as well as the loss function used to train the networks. This approach yields very low prediction errors, in particular, when using the U-Net architecture. Furthermore, the models are also able to generalize to unseen geometries of the same type. A transfer learning approach enables the model to be trained to a new type of geometries with very low training cost. Finally, based on this transfer learning approach, a sequential learning strategy is introduced, which significantly reduces the amount of necessary training data.

Full Text (PDF) [6.3 MB], BibTeX

Key words

Convolutional neural networks, computational fluid dynamics, reduced order surrogate models, U-Net, transfer learning, sequential learning

AMS subject classifications

35Q30, 68T07, 68T10, 65N22

Links to the cited ETNA articles

[15]	Vol. 56 (2022), pp. 1-27 Viktor Grimm, Alexander Heinlein, Axel Klawonn, Martin Lanser, and Janine Weber: Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks
[19]	Vol. 56 (2022), pp. 52-65 Martin W. Hess, Annalisa Quaini, and Gianluigi Rozza: A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions

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