pytorch实现CNN和Bi-Transformer时间序列预测

首先，我们需要导入必要的库。在这个例子中，我们需要使用PyTorch、NumPy和Matplotlib。

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

接下来，我们需要准备我们的时间序列数据。我们将使用sin函数生成一个周期为50的时间序列，长度为200。

# Generate time series data
TIME_STEP = 50
SIN_WAVE_AMPLITUDE = 0.5
def sin(x, t):
    return np.sin(x + t)

def toy_problem(T):
    x = np.arange(0, 2 * T + 1)
    return sin(2 * np.pi * x / T, 0), sin(2 * np.pi * x / T, 0.25), sin(2 * np.pi * x / T, 0.5)

x_train, y_train, z_train = toy_problem(TIME_STEP)

接下来，我们需要将数据转换为PyTorch张量，并将其分为训练集和测试集。

# Convert data to PyTorch tensors
x_train = torch.from_numpy(x_train).float().unsqueeze(1)
y_train = torch.from_numpy(y_train).float().unsqueeze(1)
z_train = torch.from_numpy(z_train).float().unsqueeze(1)

# Split data into training and testing sets
train_data = torch.cat((x_train, y_train, z_train), dim=1)
train_input = train_data[:, :-1]
train_target = train_data[:, 1:]

train_input = train_input.view(-1, 2, TIME_STEP)
train_target = train_target.view(-1, 2, TIME_STEP)

现在我们已经准备好了我们的数据，我们可以开始构建我们的CNN和Bi-Transformer模型。我们将使用两个序列模块来处理每个时间步长的输入，然后将它们连接起来，并使用一个线性层来生成输出。

# Define CNN and Bi-Transformer model
class CNN(nn.Module):
    def __init__(self):
        super(CNN, self).__init__()
        self.conv = nn.Conv1d(2, 16, 5, padding=2)
        self.pool = nn.MaxPool1d(2)
        self.relu = nn.ReLU()

    def forward(self, x):
        x = self.conv(x)
        x = self.relu(x)
        x = self.pool(x)
        x = self.conv(x)
        x = self.relu(x)
        x = self.pool(x)
        return x

class BiTransformer(nn.Module):
    def __init__(self):
        super(BiTransformer, self).__init__()
        self.pos_enc = PositionalEncoding(16, dropout=0.1)
        self.transformer = nn.Transformer(d_model=16, nhead=2, num_encoder_layers=2, num_decoder_layers=2, dim_feedforward=32, dropout=0.1)
        self.fc = nn.Linear(16, 1)

    def forward(self, x):
        x = self.pos_enc(x)
        x = self.transformer(x, x)
        x = self.fc(x)
        return x

class PositionalEncoding(nn.Module):
    def __init__(self, d_model, dropout=0.1, max_len=1000):
        super(PositionalEncoding, self).__init__()
        self.dropout = nn.Dropout(p=dropout)

        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len, dtype=torch.float).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, d_model, 2).float() * (-np.log(10000.0) / d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(0).transpose(0, 1)
        self.register_buffer('pe', pe)

    def forward(self, x):
        x = x + self.pe[:x.size(0), :]
        return self.dropout(x)

现在我们已经定义了我们的模型，我们可以开始训练它。我们将使用均方误差损失函数和随机梯度下降优化器。

# Train the model
model = nn.Sequential(CNN(), BiTransformer())
loss_fn = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

num_epochs = 1000
for epoch in range(num_epochs):
    optimizer.zero_grad()

    output = model(train_input)
    loss = loss_fn(output, train_target)
    loss.backward()

    optimizer.step()

    if epoch % 100 == 0:
        print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# Generate predictions
model.eval()
with torch.no_grad():
    test_input = train_data[:, :2, :]
    test_output = model(test_input)

最后，我们可以将预测结果可视化，并将其与原始数据进行比较。

# Plot predictions
plt.plot(range(TIME_STEP), test_input[0, 0, :], label='input')
plt.plot(range(TIME_STEP, 2*TIME_STEP), test_output[0, 0, :], label='prediction')
plt.plot(range(TIME_STEP, 2*TIME_STEP), test_input[0, 1, :], label='target')
plt.legend()
plt.show()

这就是如何使用PyTorch实现CNN和Bi-Transformer时间序列预测。