循环神经网络RNN
多层感知机MLP 是最为基础的，可以模拟线性变换，复杂度低，训练简单，适用范围广
而卷积神经网络CNN可以提取不太尺度的关联信息，有助于图像特征提取
循环神经网络适合数据序列大，有一定前后关联的数据特征
GRU
循环神经网络可能出现梯度消失或者梯度爆炸，解决方法之一就是GRU门控循环单元 来控制当前和过去时刻直接的关系
有一个更新单元和重置单元
重置单元可以选择的遗忘，就是将有些维度等于0，消除了过去的信息，用来选择旧信息的保留比例
更新单元就是来选择应该倾向于旧的信息还是新的输入x，接近1则保留旧的信息忽略新输入信息，接近0就是选择让新信息和旧信息混合，可以用来选择控制旧信息和新信息直接的比例
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import numpy as np
import matplotlib.pyplot as plt
from tqdm import tqdm
import torch
import torch.nn as nn
#%%
data=np.loadtxt('./data/sindata_1000.csv',delimiter=',')
num_data=len(data)
split=int(num_data*0.8)
print(split)
plt.figure
#np.arange(7)就是0 1 2 ...7
plt.scatter(np.arange(split),data[:split],color='blue',s=10,label='training')
plt.scatter(np.arange(split, num_data), data[split:], color='none',
edgecolor='orange', s=10, label='test set')
plt.xlabel('X axis')
plt.ylabel('Y axis')
plt.legend()
plt.show()
#%%
# 分割数据集
train_data = np.array(data[:split])
test_data = np.array(data[split:])
# 输入序列长度
seq_len = 20
# 处理训练数据，把切分序列后多余的部分去掉 //取整数
train_num = len(train_data) // (seq_len + 1) * (seq_len + 1)
train_data = np.array(train_data[:train_num]).reshape(-1, seq_len + 1, 1)
np.random.seed(0)
torch.manual_seed(0)
x_train = train_data[:, :seq_len] # 形状为(num_data, seq_len, input_size)
y_train = train_data[:, 1: seq_len + 1]
print(f'训练序列数：{len(x_train)}')
# 转为PyTorch张量
x_train = torch.from_numpy(x_train).to(torch.float32)
y_train = torch.from_numpy(y_train).to(torch.float32)
x_test = torch.from_numpy(test_data[:-1]).to(torch.float32)
y_test = torch.from_numpy(test_data[1:]).to(torch.float32)
#%%
class GRU(nn.Module):
# 包含PyTorch的GRU和拼接的MLP
def __init__(self, input_size, output_size, hidden_size):
super().__init__()
# GRU模块
self.gru = nn.GRU(input_size=input_size, hidden_size=hidden_size)
# 将中间变量映射到预测输出的MLP
self.linear = nn.Linear(hidden_size, output_size)
def forward(self, x, hidden):
# 前向传播
# x的维度为(batch_size, seq_len, input_size)
# GRU模块接受的输入为(seq_len, batch_size, input_size)
# 因此需要对x进行变换
# transpose函数可以交换x的坐标轴
# out的维度是(seq_len, batch_size, hidden_size)
out, hidden = self.gru(torch.transpose(x, 0, 1), hidden)
# 取序列最后的中间变量输入给全连接层
out = self.linear(out.view(-1, hidden_size))
return out, hidden
#%%
# 超参数
input_size = 1 # 输入维度
output_size = 1 # 输出维度
hidden_size = 16 # 中间变量维度
learning_rate = 5e-4
# 初始化网络
gru = GRU(input_size, output_size, hidden_size)
gru_optim = torch.optim.Adam(gru.parameters(), lr=learning_rate)
# GRU测试函数，x和hidden分别是初始的输入和中间变量
def test_gru(gru, x, hidden, pred_steps):
pred = []
inp = x.view(-1, input_size)
for i in range(pred_steps):
gru_pred, hidden = gru(inp, hidden)
pred.append(gru_pred.detach())
inp = gru_pred
return torch.concat(pred).reshape(-1)
#%%
# MLP的超参数
hidden_1 = 32
hidden_2 = 16
mlp = nn.Sequential(
nn.Linear(input_size, hidden_1),
nn.ReLU(),
nn.Linear(hidden_1, hidden_2),
nn.ReLU(),
nn.Linear(hidden_2, output_size)
)
mlp_optim = torch.optim.Adam(mlp.parameters(), lr=learning_rate)
#%%
# MLP测试函数，相比于GRU少了中间变量
def test_mlp(mlp, x, pred_steps):
pred = []
inp = x.view(-1, input_size)
for i in range(pred_steps):
mlp_pred = mlp(inp)
pred.append(mlp_pred.detach())
inp = mlp_pred
return torch.concat(pred).reshape(-1)
#%%
max_epoch = 150
criterion = nn.functional.mse_loss
hidden = None # GRU的中间变量
# 训练损失
gru_losses = []
mlp_losses = []
gru_test_losses = []
mlp_test_losses = []
# 开始训练
with tqdm(range(max_epoch)) as pbar:
for epoch in pbar:
st = 0
gru_loss = 0.0
mlp_loss = 0.0
# 随机梯度下降
for X, y in zip(x_train, y_train):
# 更新GRU模型
# 我们不需要通过梯度回传更新中间变量
# 因此将其从有梯度的部分分离出来
if hidden is not None:
hidden.detach_()
gru_pred, hidden = gru(X[None, ...], hidden)
gru_train_loss = criterion(gru_pred.view(y.shape), y)
gru_optim.zero_grad()
gru_train_loss.backward()
gru_optim.step()
gru_loss += gru_train_loss.item()
# 更新MLP模型
# 需要对输入的维度进行调整，变成(seq_len, input_size)的形式
mlp_pred = mlp(X.view(-1, input_size))
mlp_train_loss = criterion(mlp_pred.view(y.shape), y)
mlp_optim.zero_grad()
mlp_train_loss.backward()
mlp_optim.step()
mlp_loss += mlp_train_loss.item()
gru_loss /= len(x_train)
mlp_loss /= len(x_train)
gru_losses.append(gru_loss)
mlp_losses.append(mlp_loss)
# 训练和测试时的中间变量序列长度不同，训练时为seq_len，测试时为1
gru_pred = test_gru(gru, x_test[0], hidden[:, -1], len(y_test))
mlp_pred = test_mlp(mlp, x_test[0], len(y_test))
gru_test_loss = criterion(gru_pred, y_test).item()
mlp_test_loss = criterion(mlp_pred, y_test).item()
gru_test_losses.append(gru_test_loss)
mlp_test_losses.append(mlp_test_loss)
pbar.set_postfix({
'Epoch': epoch,
'GRU loss': f'{gru_loss:.4f}',
'MLP loss': f'{mlp_loss:.4f}',
'GRU test loss': f'{gru_test_loss:.4f}',
'MLP test loss': f'{mlp_test_loss:.4f}'
})
#%%
# 最终测试结果
gru_preds = test_gru(gru, x_test[0], hidden[:, -1], len(y_test)).numpy()
mlp_preds = test_mlp(mlp, x_test[0], len(y_test)).numpy()
plt.figure(figsize=(13, 5))
# 绘制训练曲线
plt.subplot(121)
x_plot = np.arange(len(gru_losses)) + 1
plt.plot(x_plot, gru_losses, color='blue',
label='GRU training loss')
plt.plot(x_plot, mlp_losses, color='red',
ls='-.', label='MLP training loss')
plt.plot(x_plot, gru_test_losses, color='blue',
ls='--', label='GRU test loss')
plt.plot(x_plot, mlp_test_losses, color='red',
ls=':', label='MLP test loss')
plt.xlabel('Training step')
plt.ylabel('Loss')
plt.legend(loc='lower left')
# 绘制真实数据与模型预测值的图像
plt.subplot(122)
plt.scatter(np.arange(split), data[:split], color='blue',
s=10, label='training set')
plt.scatter(np.arange(split, num_data), data[split:], color='none',
edgecolor='orange', s=10, label='test set')
plt.scatter(np.arange(split, num_data - 1), mlp_preds, color='violet',
marker='x', alpha=0.4, s=20, label='MLP preds')
plt.scatter(np.arange(split, num_data - 1), gru_preds, color='green',
marker='*', alpha=0.4, s=20, label='GRU preds')
plt.legend(loc='lower left')
plt.savefig('output_20_0.png')
plt.savefig('output_20_0.pdf')
plt.show()