在pytorch上构建卷积神经网络来实现VAE，并对矩阵数据进行降噪的代码

下面是一个使用PyTorch构建卷积神经网络实现VAE并对矩阵数据进行降噪的代码示例：

import torch
import torch.nn as nn
import torch.nn.functional as F

class VAE(nn.Module):
    def __init__(self, input_size, latent_size):
        super(VAE, self).__init__()

        # 定义编码器
        self.encoder = nn.Sequential(
            nn.Conv2d(1, 16, kernel_size=3, stride=2, padding=1),
            nn.ReLU(),
            nn.Conv2d(16, 32, kernel_size=3, stride=2, padding=1),
            nn.ReLU(),
            nn.Conv2d(32, 64, kernel_size=3, stride=2, padding=1),
            nn.ReLU(),
            nn.Conv2d(64, 128, kernel_size=3, stride=2, padding=1),
            nn.ReLU(),
            nn.Flatten(),
            nn.Linear(128 * (input_size // 16) ** 2, 512),
            nn.ReLU(),
            nn.Linear(512, latent_size)
        )

        # 定义解码器
        self.decoder = nn.Sequential(
            nn.Linear(latent_size, 512),
            nn.ReLU(),
            nn.Linear(512, 128 * (input_size // 16) ** 2),
            nn.ReLU(),
            nn.Unflatten(1, (128, input_size // 16, input_size // 16)),
            nn.ConvTranspose2d(128, 64, kernel_size=4, stride=2, padding=1),
            nn.ReLU(),
            nn.ConvTranspose2d(64, 32, kernel_size=4, stride=2, padding=1),
            nn.ReLU(),
            nn.ConvTranspose2d(32, 16, kernel_size=4, stride=2, padding=1),
            nn.ReLU(),
            nn.ConvTranspose2d(16, 1, kernel_size=3, stride=1, padding=1)
        )

    def encode(self, x):
        # 编码器输出均值和标准差
        h = self.encoder(x)
        mu, logvar = h.chunk(2, dim=1)
        return mu, logvar

    def reparameterize(self, mu, logvar):
        # 通过均值和标准差生成潜在向量
        std = torch.exp(0.5 * logvar)
        eps = torch.randn_like(std)
        z = mu + eps * std
        return z

    def decode(self, z):
        # 解码器输出重构结果
        x_hat = self.decoder(z)
        return x_hat

    def forward(self, x):
        # 前向传播
        mu, logvar = self.encode(x)
        z = self.reparameterize(mu, logvar)
        x_hat = self.decode(z)
        return x_hat, mu, logvar

# 训练VAE模型
def train_vae(model, train_loader, optimizer, device):
    model.train()
    train_loss = 0
    for batch_idx, data in enumerate(train_loader):
        data = data.to(device)
        optimizer.zero_grad()
        recon_batch, mu, logvar = model(data)
        loss = loss_function(recon_batch, data, mu, logvar)
        loss.backward()
        train_loss += loss.item()
        optimizer.step()
    return train_loss / len(train_loader.dataset)

# VAE模型