9-1 Deep-Learning Model for High-Resolution Steady Flow Prediction

-Convolutional Neural Networks for Multiresolution Steady Flow Prediction-

Fig.9-2 Flow

Fig.9-2 Flow field prediction with the proposed deep-learning model

The simulation (reference) and predicted two-dimensional steady-state flow fields around objects with a resolution of 10242. Here, u and v are the normalized flow velocity along the x and y axes, respectively. The arrows represent the directions of the in- and out-flows from left to right.


Fig.9-3 Architecture

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Fig.9-3 Architecture of the proposed model

The global low-resolution and patched high-resolution signed distance functions (SDFs) are fed to networks G0 and G1. The patched features (256 × 256) from G0 are merged with the down-sampled features (256 × 256) by G1 to predict the patched high-resolution flow field. Since the elementwise sum of the global features from G0 and the local features from G1 allows the propagation of the global information to G1, the predicted high-resolution flow fields maintain the consistency of the structures between the patches.


Deep-learning-based models using convolutional neural networks (CNNs) are widely used to generate photo-realistic images. These models have also been applied to surrogate models that approximate computational fluid dynamics (CFD) simulation results, which can be obtained significantly faster than CFD simulation results. A kind of surrogate models are needed for an instant prediction and large-scale parameter scans of flow fields. Because of memory-size constraints, conventional models have been applied up to a resolution of 512 × 512. For the high-resolution flow fields, a model has to predict the patched regions of flow fields independently, and this leads to inconsistency between the independently predicted flow fields.

In this work, we developed a new flow-prediction model to resolve the memory and connection issues simultaneously. A CNN-based model predicts the steady-state flow field around an object from a signed distance function (SDF), which represents both simple and complex object shapes in a universal way. Conventional models have applied CNNs to the patched SDF data to predict the patched flow field. In this work, we developed a model to use a low-resolution global SDF and a high-resolution patched SDF to predict a globally consistent high-resolution flow field (Fig.9-2).

Here, the low-resolution SDF is constructed from a high-resolution SDF by down-sampling.

In CNNs, the input data are first encoded and then decoded to the target output data. The developed model consists of an encoder/decoder (G0) for low-resolution data and another encoder/decoder (G1) for high-resolution patched data (Fig.9-3). Figure 9-3 shows the prediction of the flow field with 1024 × 1024 resolution, where a low-resolution (512 × 512) global SDF and a high-resolution (512 × 512) patched SDF (1/4 region) are used as input data to G0 and G1, respectively. The patched features (256 × 256) from G0 are merged with the down-sampled features (256 × 256) by G1. By combining the global information from the low-resolution data and the local structures from the high-resolution patched data, the model can predict the global high-resolution flow field consistently. Although such a model has also been proposed in the field of image processing, it uses the global low-resolution and high-resolution data. Our model is more memory-efficient and can still predict the global high-resolution flow field by using the patched high-resolution data. Using this model, we can predict the flow fields instantly and perform large-scale parameter scans.

This work was partly supported by Joint Usage/Research Center for Interdisciplinary Large-Scale Information Infrastructures (Project ID: jh210049-MDH).

(Yuichi Asahi)


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