利用在pytorch框架下，写出利用卷积神经网络实现手写数字识别，使用两种不同的神经网络进行训练并比较测试结果的代码

好的，下面是基于PyTorch实现手写数字识别的代码，其中使用了两种不同的卷积神经网络模型进行训练，并比较测试结果的准确率。

首先，我们需要导入必要的Python库和模块：

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt

然后，我们可以定义一些超参数，包括批次大小、学习率、训练轮数等：

batch_size = 128
learning_rate = 0.001
num_epochs = 10

接下来，我们可以下载并加载MNIST手写数字数据集，并将其进行预处理：

# 定义数据预处理
transform = transforms.Compose(
    [transforms.ToTensor(),
     transforms.Normalize((0.5,), (0.5,))])

# 加载MNIST数据集
trainset = torchvision.datasets.MNIST(root='./data', train=True,
                                        download=True, transform=transform)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=batch_size,
                                          shuffle=True, num_workers=2)

testset = torchvision.datasets.MNIST(root='./data', train=False,
                                       download=True, transform=transform)
testloader = torch.utils.data.DataLoader(testset, batch_size=batch_size,
                                         shuffle=False, num_workers=2)

然后，我们可以定义两个不同的卷积神经网络模型，分别为LeNet-5和VGG-16：

# 定义LeNet-5模型
class LeNet5(nn.Module):
    def __init__(self):
        super(LeNet5, self).__init__()
        self.conv1 = nn.Conv2d(1, 6, 5)
        self.pool1 = nn.MaxPool2d(2, 2)
        self.conv2 = nn.Conv2d(6, 16, 5)
        self.pool2 = nn.MaxPool2d(2, 2)
        self.fc1 = nn.Linear(16 * 4 * 4, 120)
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        x = self.pool1(torch.relu(self.conv1(x)))
        x = self.pool2(torch.relu(self.conv2(x)))
        x = x.view(-1, 16 * 4 * 4)
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

# 定义VGG-16模型
class VGG16(nn.Module):
    def __init__(self):
        super(VGG16, self).__init__()
        self.conv1 = nn.Conv2d(1, 64, 3, padding=1)
        self.conv2 = nn.Conv2d(64, 64, 3, padding=1)
        self.pool1 = nn.MaxPool2d(2, 2)
        self.conv3 = nn.Conv2d(64, 128, 3, padding=1)
        self.conv4 = nn.Conv2d(128, 128, 3, padding=1)
        self.pool2 = nn.MaxPool2d(2, 2)
        self.conv5 = nn.Conv2d(128, 256, 3, padding=1)
        self.conv6 = nn.Conv2d(256, 256, 3, padding=1)
        self.conv7 = nn.Conv2d(256, 256, 3, padding=1)
        self.pool3 = nn.MaxPool2d(2, 2)
        self.conv8 = nn.Conv2d(256, 512, 3, padding=1)
        self.conv9 = nn.Conv2d(512, 512, 3, padding=1)
        self.conv10 = nn.Conv2d(512, 512, 3, padding=1)
        self.pool4 = nn.MaxPool2d(2, 2)
        self.conv11 = nn.Conv2d(512, 512, 3, padding=1)
        self.conv12 = nn.Conv2d(512, 512, 3, padding=1)
        self.conv13 = nn.Conv2d(512, 512, 3, padding=1)
        self.pool5 = nn.MaxPool2d(2, 2)
        self.fc1 = nn.Linear(512, 4096)
        self.fc2 = nn.Linear(4096, 4096)
        self.fc3 = nn.Linear(4096, 10)

    def forward(self, x):
        x = torch.relu(self.conv1(x))
        x = torch.relu(self.conv2(x))
        x = self.pool1(x)
        x = torch.relu(self.conv3(x))
        x = torch.relu(self.conv4(x))
        x = self.pool2(x)
        x = torch.relu(self.conv5(x))
        x = torch.relu(self.conv6(x))
        x = torch.relu(self.conv7(x))
        x = self.pool3(x)
        x = torch.relu(self.conv8(x))
        x = torch.relu(self.conv9(x))
        x = torch.relu(self.conv10(x))
        x = self.pool4(x)
        x = torch.relu(self.conv11(x))
        x = torch.relu(self.conv12(x))
        x = torch.relu(self.conv13(x))
        x = self.pool5(x)
        x = x.view(-1, 512)
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = self.fc3(x)
        return x

接下来，我们可以定义训练函数和测试函数，用于训练和测试模型：

# 定义训练函数
def train(model, trainloader, criterion, optimizer, num_epochs):
    for epoch in range(num_epochs):
        running_loss = 0.0
        for i, data in enumerate(trainloader, 0):
            inputs, labels = data
            optimizer.zero_grad()
            outputs = model(inputs)
            loss = criterion(outputs, labels)
            loss.backward()
            optimizer.step()
            running_loss += loss.item()
        print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, running_loss/len(trainloader)))

# 定义测试函数
def test(model, testloader):
    correct = 0
    total = 0
    with torch.no_grad():
        for data in testloader:
            images, labels = data
            outputs = model(images)
            _, predicted = torch.max(outputs.data, 1)
            total += labels.size(0)
            correct += (predicted == labels).sum().item()
    print('Accuracy: {:.2f}%'.format(100 * correct / total))

最后，我们可以定义主函数，用于训练和测试LeNet-5和VGG-16模型：

if __name__ == '__main__':
    # 定义LeNet-5模型、损失函数和优化器
    lenet5 = LeNet5()
    criterion = nn.CrossEntropyLoss()
    optimizer = optim.Adam(lenet5.parameters(), lr=learning_rate)

    # 训练和测试LeNet-5模型
    print('Training LeNet-5...')
    train(lenet5, trainloader, criterion, optimizer, num_epochs)
    print('Testing LeNet-5...')
    test(lenet5, testloader)

    # 定义VGG-16模型、损失函数和优化器
    vgg16 = VGG16()
    criterion = nn.CrossEntropyLoss()
    optimizer = optim.Adam(vgg16.parameters(), lr=learning_rate)

    # 训练和测试VGG-16模型
    print('Training VGG-16...')
    train(vgg16, trainloader, criterion, optimizer, num_epochs)
    print('Testing VGG-16...')
    test(vgg16, testloader)

运行上述代码，即可训练和测试LeNet-5和VGG-16模型，并比较它们的测试准确率。