使用PyTorch实现一个简单的卷积神经网络（CNN），用于识别手写数字（使用MNIST数据集）。

使用PyTorch实现一个简单的卷积神经网络（CNN）来识别手写数字（使用MNIST数据集）的基本步骤如下：

1. 导入必要的库：

import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torchvision import datasets, transforms

2. 定义一个卷积神经网络模型：

class SimpleCNN(nn.Module):
    def __init__(self):
        super(SimpleCNN, self).__init__()
        self.conv1 = nn.Conv2d(1, 32, kernel_size=3, stride=1, padding=1)
        self.conv2 = nn.Conv2d(32, 64, kernel_size=3, stride=1, padding=1)
        self.fc1 = nn.Linear(7*7*64, 1024)
        self.fc2 = nn.Linear(1024, 10)

    def forward(self, x):
        x = F.max_pool2d(F.relu(self.conv1(x)), 2)
        x = F.max_pool2d(F.relu(self.conv2(x)), 2)
        x = x.view(-1, 7*7*64)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return x

3. 准备数据：

transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])

train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)
test_dataset = datasets.MNIST(root='./data', train=False, download=True, transform=transform)

train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=64, shuffle=True)
test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=1000, shuffle=False)

4. 初始化网络和优化器：

model = SimpleCNN()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

5. 训练网络：

def train(model, device, train_loader, optimizer, epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)
        optimizer.zero_grad()
        output = model(data)
        loss = F.cross_entropy(output, target)
        loss.backward()
        optimizer.step()
        
        if batch_idx % 10 == 0:
            print(f'Train Epoch: {epoch} [{batch_idx * len(data)}/{len(train_loader.dataset)} ({100. * batch_idx / len(train_loader):.0f}%)]\tLoss: {loss.item():.6f}')

6. 测试网络：

def test(model, device, test_loader):
    model.eval()
    test_loss = 0
    correct = 0
    with torch.no_grad():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)
            test_loss += F.cross_entropy(output, target, reduction='sum').item()  # sum up batch loss
            pred = output.argmax(dim=1, keepdim=True)  # get the index of the max log-probability
            correct += pred.eq(target.view_as(pred)).sum().item()

    test_loss /= len(test_loader.dataset)
    print(f'\nTest set: Average loss: {test_loss:.4f}, Accuracy: {correct}/{len(test_loader.dataset)} ({100. * correct / len(test_loader.dataset):.0f}%)\n')

7. 运行训练和测试：

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model.to(device)

for epoch in range(1, 10):
    train(model, device, train_loader, optimizer, epoch)
    test(model, device, test_loader)

以上代码展示了如何使用PyTorch搭建一个简单的CNN模型，并在MNIST数据集上进行训练和测试。请确保你的环境中已经安装了PyTorch和torchvision库，并且拥有一个可用的GPU（如果选择使用）。