Surrogate convolutional neural network models for steady computational fluid dynamics simulations

Electronic Transactions on Numerical Analysis

article

Matthias Eichinger¹  Alexander Heinlein²  Axel Klawonn¹ 

[1] Department of Mathematics and Computer Science, University of Cologne;Delft Institute of Applied Mathematics, Delft University of Technology;Center for Data and Simulation Science, University of Cologne

关键词: Convolutional neural networks;    computational fluid dynamics;    reduced order surrogate models;    U-Net;    transfer learning;    sequential learning;   

DOI  :  10.1553/etna_vol56s235

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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.

【 授权许可】

Unknown