---license: Apache License 2.0 tasks:- Domain-Specific Large Models- Fluid Dynamics---# 1. DeepCFD 模型简介计算流体力学（Computational fluid dynamics, CFD）通过求解Navier-Stokes方程（N-S方程），可以获得流体的各种物理量的分布，如密度、压力和速度等，在微电子系统、土木工程和航空航天等领域应用广泛。然而，在某些复杂的应用场景中，如机翼优化和流体与结构相互作用方面，需要使用千万级甚至上亿的网格对问题进行建模（如下图所示，下图展示了F-18战斗机的全机内外流一体结构化网格模型），导致CFD的计算量非常巨大。因此，目前亟需发展出一种相比于传统CFD方法更高效，且可以保持计算精度的方法。这篇文章的作者提到，可以使用深度学习的方法，通过训练少量传统CFD仿真的数据，构建一种数据驱动（data-driven）的CFD计算模型，来解决上述的问题。<img src="http://www.cannews.com.cn/files/Resource/attachement/2017/0511/1494489582596.jpg" alt="img" style="zoom:80%;" />本模型是针对论文：[DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks](https://arxiv.org/abs/2004.08826)[J]基于飞桨框架进行模型复现，文中作者提出了一个基于卷积神经网络（Convolutional neural networks, CNN）的CFD计算模型，称作DeepCFD，该模型可以同时计算流体流过任意障碍物的流场。该方法有以下几个特点：1. DeepCFD本质上是一种基于CNN的代理模型，可以用于快速计算二维非均匀稳态层流流动，相比于传统的CFD方法，该方法可以在保证计算精度的情况下达到至少三个数量级的加速。2. DeepCFD可以同时计算流体在x方向和y方向的流体速度，同时还能计算流体压强。3. 训练该模型的数据由OpenFOAM（一种开源CFD计算软件）计算得到。# 2. 模型效果及应用场景# 3. 模型如何使用## 3.1 环境安装* 硬件：GPU、CPU* 框架：PaddlePaddle >= 2.0.0## 3.2 数据集数据集使用原作者利用OpenFOAM计算的CFD算例，共981组，分为两个文件（dataX.pkl, dataY.pkl），两个文件大小都是152 MB，形状均为[981, 3, 172, 79]。dataX.pkl包括三种输入：障碍物的SDF、计算域边界的SDF和流动区域的标签；dataY.pkl包括三种输出：流体的x方向速度、y方向速度和流体压强。数据获取使用的计算网格为172×79。数据集地址：https://aistudio.baidu.com/aistudio/datasetdetail/162674或https://www.dropbox.com/s/kg0uxjnbhv390jv/Data_DeepCFD.7z?dl=0本示例数据集已经保存在百度云环境中，可直接使用，在项目clone之后，数据集存储在项目路径下。示意代码为```dataset = 'https://deepcfd-data.bj.bcebos.com/dataset.zip'!wget dataset```## 3.3 快速开始**step1：克隆本项目**以下方式可以二选一：* 搜索DeepCFD_with_PaddlePaddle，选择对应的版本，Fork.![fork.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/fork.png?raw=true) 选择目标路径，代码如下：```% cd ./DeepCFD_with_PaddlePaddle/```* git clone 项目 notebook上命令如下：```!git clone https://github.com/zbyandmoon/DeepCFD_with_PaddlePaddle/%cd ./DeepCFD_with_PaddlePaddle/``````python# 默认使用git clone方式，如基于已有的aistudio项目fork，可注释之后的git clone部分# %cd ~# %cd ./DeepCFD_with_PaddlePaddle/``````python# 若选择git clone的方式，则忽略fork部分的操作和脚本，使用如下脚本（默认使用git方式,若repo链接较慢，可多试几次）%cd ~!git clone https://github.com/zbyandmoon/DeepCFD_with_PaddlePaddle/%cd ./DeepCFD_with_PaddlePaddle/```**step2：数据集加载**执行以下脚本，将服务器数据下载到工作路径下```python%cd ./data!wget https://deepcfd-data.bj.bcebos.com/dataset.zip!unzip dataset.zip```**step3：开始训练**确认在正确路径后，执行如下命令**单卡训练**```pythonpython -m paddle.distributed.launch --gpus=0 train.py```**多卡训练**以四卡为例```pythonpython -m paddle.distributed.launch --gpus=0,1,2,3 train.py```结果保存在result文件中（注：result文件夹中已经包含了一个完整的训练过程，可在训练前将其清空）。多卡训练会额外生成一个./log/文件夹，存放训练日志```python.├── log│ ├── workerlog.0│ ├── workerlog.1│ ├── workerlog.2│ └── workerlog.3└── train.py```部分训练日志如下所示```pythonEpoch #1 Train Loss = 884808909.0 Train Total MSE = 10197.3000353043 Train Ux MSE = 3405.3426083044824 Train Uy MSE = 4334.0962839376825 Train p MSE = 2457.8616943359375 Validation Loss = 53205074.5 Validation Total MSE = 1027.7523040254237 Validation Ux MSE = 419.7688029661017 Validation Uy MSE = 543.9674920550848 Validation p MSE = 64.01604872881356Epoch #2 Train Loss = 75408434.25 Train Total MSE = 603.198411591199 Train Ux MSE = 277.9321616481414 Train Uy MSE = 303.4222437021684 Train p MSE = 21.843986488987337 Validation Loss = 17892356.5 Validation Total MSE = 312.7194186970339 Validation Ux MSE = 169.64230501853814 Validation Uy MSE = 140.46789757680085 Validation p MSE = 2.6092084981627384``````python#单卡%cd ..!python train.py``````python#四卡# !python -m paddle.distributed.launch --gpus=0,1,2,3 train.py```**step4：评估模型**```pythonpython eval.py```此时的输出为：```pythonTotal MSE is 1.895322561264038, Ux MSE is 0.6951090097427368, Uy MSE is 0.21001490950584412, p MSE is 0.9901986718177795``````python!python eval.py```**step5：使用预训练模型预测**考虑到需要展示流场图像对比结果，在Jupyter notebook环境中运行如下代码进行结果输出。某个障碍物的流场预测结果展示如下：![paddle_contour.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/paddle_contour.png?raw=true)```python# 本文件用于使用训练好的模型预测流场import picklefrom utils.train_functions import *from utils.functions import *from model.UNetEx import UNetEximport configparserconfig = configparser.ConfigParser()config.read("./config/config.ini")``` /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/__init__.py:107: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working from collections import MutableMapping /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/rcsetup.py:20: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working from collections import Iterable, Mapping /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/colors.py:53: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working from collections import Sized ['./config/config.ini']```python# 设置卷积核大小kernel_size = int(config["net_parameter"]["kernel_size"])# 设置卷积层channel数目filters = [int(i) for i in config["net_parameter"]["filters"].split(",")]# 设置batch_norm和weight_normbn = bool(int(config["net_parameter"]["batch_norm"]))wn = bool(int(config["net_parameter"]["weight_norm"]))# 构建模型model = UNetEx(3, 3, filters=filters, kernel_size=kernel_size, batch_norm=bn, weight_norm=wn)# 加载模型参数model.set_state_dict( paddle.load(os.path.join(config["path"]["save_path"], config["path"]["model_name"])))# 加载数据集并处理x = pickle.load(open(os.path.join(config["path"]["data_path"], "dataX.pkl"), "rb"))y = pickle.load(open(os.path.join(config["path"]["data_path"], "dataY.pkl"), "rb"))x = paddle.to_tensor(x, dtype="float32")y = paddle.to_tensor(y, dtype="float32")y_trans = paddle.transpose(y, perm=[0, 2, 3, 1])channels_weights = paddle.reshape( paddle.sqrt(paddle.mean(paddle.transpose(y, perm=[0, 2, 3, 1]).reshape((981 * 172 * 79, 3)) ** 2, axis=0)), shape=[1, -1, 1, 1])# 按7：3的比例分割数据集，7为训练集，3为测试集train_data, test_data = split_tensors(x, y, ratio=float(config["hyperparameter"]["train_test_ratio"]))train_dataset, test_dataset = paddle.io.TensorDataset([train_data[0], train_data[1]]), paddle.io.TensorDataset( [test_data[0], test_data[1]])test_x, test_y = test_dataset[:]``` W1121 16:09:58.850512 192 gpu_resources.cc:61] Please NOTE: device: 0, GPU Compute Capability: 7.0, Driver API Version: 11.2, Runtime API Version: 11.2 W1121 16:09:58.854226 192 gpu_resources.cc:91] device: 0, cuDNN Version: 8.2.```python# 测试训练模型out = model(test_x)# 计算残差error = paddle.abs(out.cpu() - test_y.cpu())# 作出CFD和CNN的计算结果对比图以及对应的残差图(s可修改)s = 0visualize(test_y.detach().numpy(), out.detach().numpy(), error.detach().numpy(), s)``` /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:2349: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working if isinstance(obj, collections.Iterator): /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:2366: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated, and in 3.8 it will stop working return list(data) if isinstance(data, collections.MappingView) else data /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/colors.py:101: DeprecationWarning: np.asscalar(a) is deprecated since NumPy v1.16, use a.item() instead ret = np.asscalar(ex) /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/image.py:425: DeprecationWarning: np.asscalar(a) is deprecated since NumPy v1.16, use a.item() instead a_min = np.asscalar(a_min.astype(scaled_dtype)) /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages/matplotlib/image.py:426: DeprecationWarning: np.asscalar(a) is deprecated since NumPy v1.16, use a.item() instead a_max = np.asscalar(a_max.astype(scaled_dtype)) ![png](output_14_1.png) ## 3.4 代码结构与参数说明### 3.4.1 代码结构```pythonDeepCFD_with_PaddlePaddle├─ config│ └─ config.ini├─ data│ └─ README.md├─ model│ └─ UNetEx.py├─ result│ ├─ DeepCFD_965.pdparams│ ├─ results.json│ └─ train_log.txt└─ utils ├─ functions.py └─ train_functions.py ├─ README.md├─ README_cn.md├─ eval.py├─ train.py├─ predict.ipynb├─ requirements.txt```### 3.4.2 参数说明可以在/DeepCFD_with_PaddlePaddle/config/config.ini中设置训练的参数，包括以下内容：| 参数 | 推荐值 | 额外说明 || ---------------- | -------------------- | --------------------------------------------- || batch_size | 64 | || train_test_ratio | 0.7 | 训练集占数据集的比例，0.7即训练集70%测试集30% || learning_rate | 0.001 | || weight_decay | 0.005 | AdamW专用，若修改优化算法需要修改train.py || epochs | 1000 | || kernel_size | 5 | 卷积核大小 || filters | 8, 16, 32, 32 | 卷积层channel数目 || batch_norm | 0 | 批量正则化，0为False，1为True || weight_norm | 0 | 权重正则化，0为False，1为True || data_path | ./data | 数据集路径，视具体情况设置 || save_path | ./result | 模型和训练记录的保存路径，视具体情况设置 || model_name | DeepCFD_965.pdparams | 具体加载的模型名称，后缀不能省略 |## 3.5 预测结果下图展示了原文的预测结果，文中评价模型的优劣共包含四个指标：Total MSE、Ux MSE、Uy MSE、p MSE（MSE的意思是均方根误差）。![metrics.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/metrics.png?raw=true)下图展示了某种形状障碍物的CFD（注：simpleFOAM是OpenFOAM求解器的一种）和DeepCFD流场计算结果对比。![pytorch_contour.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/pytorch_contour.png?raw=true)# 4. 模型原理下面两张图分别为该方法的计算示意图和网络结构图。文中使用的DeepCFD网络基本结构为有3个输入和3个输出的U-net型网络。该模型输入为计算域中障碍物的符号距离函数（Signed distance function, SDF）、计算域边界的SDF和流动区域的标签；输出为流体的x方向速度、y方向速度以及流体压强。该模型的基本原理就是利用编码器部分的卷积层将3个输入下采样，变为中间量，然后使用相同结构的解码器中的反卷积层将中间量上采样为3个流体物理量输出。![compute_process.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/compute_process.png?raw=true)![DeepCFD_Net.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/DeepCFD_Net.png?raw=true)# 5. 注意事项## 5.1 模型验收标准复现的验收标准如下：![standard.png](https://github.com/zbyandmoon/Picture/blob/main/picture_DeepCFD/standard.png?raw=true)## 5.2 指标实现情况复现的实现指标如下：```pythonTotal MSE = 1.8955801725387573Ux MSE = 0.6953578591346741Uy MSE = 0.21001338958740234p MSE = 0.9902092218399048```其中，Total MSE、Ux MSE和Uy MSE在验收标准范围内，p MSE略小于验收标准的最小值。## 5.3 复现地址论文复现地址：AI Studio: https://aistudio.baidu.com/aistudio/projectdetail/4400677?contributionType=1github: https://github.com/zbyandmoon/DeepCFD_with_PaddlePaddle/tree/main/paddle```python```