用pytorch写一个全连接神经网络的mnist识别

以下是一个使用PyTorch编写的全连接神经网络的MNIST识别示例：

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

# 定义超参数
batch_size = 64
learning_rate = 0.01
num_epochs = 10

# 载入MNIST数据集
transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))])
train_dataset = datasets.MNIST(root='./data/', train=True, transform=transform, download=True)
test_dataset = datasets.MNIST(root='./data/', train=False, transform=transform, download=True)
train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=batch_size, shuffle=False)

# 定义全连接神经网络模型
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.fc1 = nn.Linear(28*28, 512)
        self.fc2 = nn.Linear(512, 256)
        self.fc3 = nn.Linear(256, 10)
        self.relu = nn.ReLU()
        self.dropout = nn.Dropout(p=0.5)

    def forward(self, x):
        x = x.view(-1, 28*28)
        x = self.relu(self.fc1(x))
        x = self.dropout(x)
        x = self.relu(self.fc2(x))
        x = self.dropout(x)
        x = self.fc3(x)
        return x

model = Net()

# 定义优化器和损失函数
criterion = nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=learning_rate)

# 训练模型
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):
        # 前向传播、计算损失、反向传播、更新权重
        outputs = model(images)
        loss = criterion(outputs, labels)
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

        # 打印训练日志
        if (i+1) % 100 == 0:
            print("Epoch [{}/{}], Step [{}/{}], Loss: {:.4f}".format(epoch+1, num_epochs, i+1, len(train_loader), loss.item()))

# 测试模型
model.eval()
with torch.no_grad():
    correct = 0
    total = 0
    for images, labels in test_loader:
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()
    print('Test Accuracy of the model on the 10000 test images: {} %'.format(100 * correct / total))

该模型定义了一个具有3个全连接层的神经网络模型，其中第一层具有512个神经元，第二层具有256个神经元，第三层输出10个类别的概率分布。模型使用ReLU激活函数和Dropout正则化。在训练过程中，使用了交叉熵损失函数和随机梯度下降优化器。最终，在测试集上计算了模型的准确度。