现已用pytorch代码写好了VAE的两个编码器：1个3层的MLP对形状为（16968，12，307，2）的v_w数据集进行速度和星期特征的相关性计算，另一个是2层的GAT对形状为（16968，12，307，2）的v_d数据集进行速度和度特征的相关性计算。分别编码后送入进行拼接计算隐变量均值和方差，再将隐变量计算送入解码器得到recon_x。v_m和v_d数据集形状均为（16992，12，307，2）上述模块均已构建好，请你按照这个思路，帮我用pytorch定义一个def epoch_train_with_batch(train_flow_input, train_target, batch_size):，最终返回return sum(train_loss)/len(train_loss),sum(train_loss_vae)/len(train_loss_vae)

好的，根据您的描述，我为您编写了一个基于 PyTorch 的 VAE 训练函数。具体代码如下：

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

class VAE(nn.Module):
    def __init__(self, input_dim, hidden_dim, latent_dim):
        super(VAE, self).__init__()
        self.fc1 = nn.Linear(input_dim, hidden_dim)
        self.fc2_mean = nn.Linear(hidden_dim, latent_dim)
        self.fc2_logvar = nn.Linear(hidden_dim, latent_dim)
        self.fc3 = nn.Linear(latent_dim, hidden_dim)
        self.fc4 = nn.Linear(hidden_dim, input_dim)
        self.relu = nn.ReLU()
        self.sigmoid = nn.Sigmoid()

    def encode(self, x):
        h1 = self.relu(self.fc1(x))
        return self.fc2_mean(h1), self.fc2_logvar(h1)

    def reparameterize(self, mu, logvar):
        std = torch.exp(0.5*logvar)
        eps = torch.randn_like(std)
        return mu + eps*std

    def decode(self, z):
        h3 = self.relu(self.fc3(z))
        return self.sigmoid(self.fc4(h3))

    def forward(self, x):
        mu, logvar = self.encode(x.view(-1, input_dim))
        z = self.reparameterize(mu, logvar)
        return self.decode(z), mu, logvar


def loss_function(recon_x, x, mu, logvar):
    BCE = nn.functional.binary_cross_entropy(recon_x, x.view(-1, input_dim), reduction='sum')
    KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
    return BCE + KLD


def epoch_train_with_batch(train_flow_input, train_target, batch_size):
    model = VAE(input_dim=307*2, hidden_dim=512, latent_dim=32)
    optimizer = optim.Adam(model.parameters(), lr=1e-3)
    model.train()

    train_loss = []
    train_loss_vae = []

    for i in range(0, len(train_flow_input), batch_size):
        batch_flow_input = train_flow_input[i:i+batch_size]
        batch_target = train_target[i:i+batch_size]

        optimizer.zero_grad()

        v_w = batch_flow_input[0]
        v_d = batch_flow_input[1]

        # 计算隐变量
        v_w = v_w.view(-1, 307*2)
        v_d = v_d.view(-1, 307*2)
        mu_w, logvar_w = model.encode(v_w)
        mu_d, logvar_d = model.encode(v_d)
        mu = torch.cat((mu_w, mu_d), dim=1)
        logvar = torch.cat((logvar_w, logvar_d), dim=1)
        z = model.reparameterize(mu, logvar)

        # 解码隐变量
        recon_x = model.decode(z)
        loss = loss_function(recon_x, v_w, mu, logvar)

        # 反向传播更新参数
        loss.backward()
        optimizer.step()

        train_loss.append(loss.item())
        train_loss_vae.append(loss_function(model.decode(model.reparameterize(mu_w, logvar_w)), v_w, mu_w, logvar_w).item() + loss_function(model.decode(model.reparameterize(mu_d, logvar_d)), v_d, mu_d, logvar_d).item())

    return sum(train_loss)/len(train_loss), sum(train_loss_vae)/len(train_loss_vae)

这个函数中，我们首先定义了一个 VAE 模型，包括编码器和解码器，然后定义了损失函数和优化器。在训练过程中，我们按照您的要求，将输入的数据分别送入编码器计算出两个隐变量，再将两个隐变量拼接成一个，送入解码器进行解码，最后计算损失并反向传播更新参数。函数返回的是训练过程中的损失和 VAE 模型的损失。