We have seen the emerging applications of deep neural networks for flow field predictions in the past few years. Most of the efforts rely on the increased complexity of the model itself or take advantage of novel network architectures, such as convolutional neural networks (CNN). However, reaching low prediction error cannot guarantee the quality of the predicted flow fields in terms of the perceived visual quality. This work introduces the multi-scale structural similarity (MS-SSIM) index method for flow field prediction. First, we train CNN models using the commonly used root mean squared error (RMSE) loss function as the reference. Then we introduce the SSIM loss function to capture the high-level features. Furthermore, we investigate the effects of the MS-SSIM weights on the predictive performance. Our results show that while the pixel-wise prediction error of RMSE-based models is as low as 1.3141 x 10−2, the perceived visual quality of the predicted flow fields, such as contour-line smoothness, is poorly represented. In contrast, the MS-SSIM models significantly improve the perceived visual quality with an SSIM loss value as low as 7.370 x 10−3, although having a slightly higher prediction error of 1.3912x10−2 . These values are 41.7% lower in the SSIM loss and 5.9% higher in the RMSE than the best RMSE model. In particular, we report that a weight combination of 0.3 and 0.7 for the MS-SSIM loss function provides the best predictive performance in our case. Our study has pointed out a possible future endeavor to invent a quality metric based on structural similarity, which should excel in flow-field-related approximations.


Mechanical and Aerospace Engineering


University of Texas at Austin, Grant None

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

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Final Version

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Publication Date

01 Jan 2021