给出一个基于pytorch的随机梯度下降SGD应用的代码

import torch
import torch.nn as nn
import torch.optim as optim

# 定义一个简单的线性模型
class LinearModel(nn.Module):
    def __init__(self, input_size, output_size):
        super(LinearModel, self).__init__()
        self.linear = nn.Linear(input_size, output_size)

    def forward(self, x):
        return self.linear(x)

# 超参数设置
input_size = 10
output_size = 1
learning_rate = 0.01
epochs = 100

# 创建模型实例
model = LinearModel(input_size, output_size)

# 定义损失函数和优化器
criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=learning_rate)

# 生成模拟数据
x = torch.randn(100, input_size)
y = torch.randn(100, output_size)

# 训练模型
for epoch in range(epochs):
    # 前向传播
    outputs = model(x)
    loss = criterion(outputs, y)

    # 反向传播和优化
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    # 打印损失值
    if (epoch+1) % 10 == 0:
        print(f'Epoch [{epoch+1}/{epochs}], Loss: {loss.item():.4f}')