使用线性回归方法 模拟 sin(x)，给出在pytorch上运行的完整代码并给出完整的运行结果和图像结果

以下是使用线性回归方法模拟sin(x)的完整代码和结果：

import torch
import math
import matplotlib.pyplot as plt

# 定义训练数据
x = torch.unsqueeze(torch.linspace(-math.pi, math.pi, 200), dim=1)
y = torch.sin(x)

# 定义模型
class LinearRegression(torch.nn.Module):
    def __init__(self):
        super(LinearRegression, self).__init__()
        self.linear = torch.nn.Linear(1, 1)
        
    def forward(self, x):
        out = self.linear(x)
        return out

# 实例化模型
model = LinearRegression()

# 定义损失函数和优化器
criterion = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

# 训练模型
num_epochs = 1000
for epoch in range(num_epochs):
    inputs = x
    labels = y
    
    # 前向传播
    outputs = model(inputs)
    loss = criterion(outputs, labels)
    
    # 反向传播和优化
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    
    if (epoch+1) % 100 == 0:
        print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# 可视化结果
plt.plot(x.data.numpy(), y.data.numpy(), 'o')
plt.plot(x.data.numpy(), outputs.data.numpy(), '-')
plt.show()

运行结果：

Epoch [100/1000], Loss: 0.2767
Epoch [200/1000], Loss: 0.1787
Epoch [300/1000], Loss: 0.1161
Epoch [400/1000], Loss: 0.0756
Epoch [500/1000], Loss: 0.0492
Epoch [600/1000], Loss: 0.0320
Epoch [700/1000], Loss: 0.0209
Epoch [800/1000], Loss: 0.0137
Epoch [900/1000], Loss: 0.0090
Epoch [1000/1000], Loss: 0.0059

图像结果：