如何在Pytorch / Python中实现多项式回归

import torch
import torch.nn as nn
import numpy as np

# 定义输入数据
x = torch.tensor([1, 2, 3, 4, 5], dtype=torch.float32)
# 定义目标数据
y = torch.tensor([2, 4, 6, 8, 10], dtype=torch.float32)

class PolynomialRegression(nn.Module):
    def __init__(self, degree):
        super(PolynomialRegression, self).__init__()
        self.degree = degree
        self.fc = nn.Linear(degree, 1)
    
    def forward(self, x):
        x = x.unsqueeze(1)
        x = torch.cat([x ** i for i in range(1, self.degree + 1)], dim=1)
        return self.fc(x)

# 设置多项式的阶数
degree = 3
# 初始化模型
model = PolynomialRegression(degree)
# 定义损失函数
criterion = nn.MSELoss()

# 定义优化器
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

# 设置训练轮数
num_epochs = 1000

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

# 预测
predicted = model(x)
# 打印预测结果
print('Predicted values:', predicted.detach().numpy())