1.問題描述
已知[k,k+n)時刻的正弦函數，預測[k+t,k+n+t)時刻的正弦曲線。
因為每個時刻曲線上的點是一個值，即feature_len=1，如果給出50個時刻的點，即seq_len=50，如果只提供一條曲線供輸入，即batch=1。輸入的shape=[seq_len, batch, feature_len] = [50, 1, 1]。
2.代碼實現
1 import numpy as np 2 import torch 3 import torch.nn as nn 4 import torch.optim as optim 5 from matplotlib import pyplot as plt 6 7 8 input_size = 1 9 hidden_size = 16 10 output_size = 1 11 12 13 class Net(nn.Module): 14 15 def __init__(self, ): 16 super(Net, self).__init__() 17 18 self.rnn = nn.RNN( 19 input_size=input_size, #feature_len=1 20 hidden_size=hidden_size, #隱藏記憶單元尺寸hidden_len 21 num_layers=1, #層數 22 batch_first=True, #在傳入數據時,按照[batch,seq_len,feature_len]的格式 23 ) 24 for p in self.rnn.parameters(): #對RNN層的參數做初始化 25 nn.init.normal_(p, mean=0.0, std=0.001) 26 27 self.linear = nn.Linear(hidden_size, output_size) #輸出層 28 29 30 def forward(self, x, hidden_prev): 31 ''' 32 x：一次性輸入所有樣本所有時刻的值(batch,seq_len,feature_len) 33 hidden_prev：第一個時刻空間上所有層的記憶單元(batch,num_layer,hidden_len) 34 輸出out(batch,seq_len,hidden_len)和hidden_prev(batch,num_layer,hidden_len) 35 ''' 36 out, hidden_prev = self.rnn(x, hidden_prev) 37 #因為要把輸出傳給線性層處理，這里將batch和seq_len維度打平，再把batch=1添加到最前面的維度（為了和y做MSE） 38 out = out.view(-1, hidden_size) #[batch=1,seq_len,hidden_len]->[seq_len,hidden_len] 39 out = self.linear(out) #[seq_len,hidden_len]->[seq_len,feature_len=1] 40 out = out.unsqueeze(dim=0) #[seq_len,feature_len=1]->[batch=1,seq_len,feature_len=1] 41 return out, hidden_prev 42 43 44 #訓練過程 45 lr=0.01 46 47 model = Net() 48 criterion = nn.MSELoss() 49 optimizer = optim.Adam(model.parameters(), lr) 50 51 hidden_prev = torch.zeros(1, 1, hidden_size) #初始化記憶單元h0[batch,num_layer,hidden_len] 52 num_time_steps = 50 #區間內取多少樣本點 53 54 for iter in range(6000): 55 start = np.random.randint(3, size=1)[0] #在0~3之間隨機取開始的時刻點 56 time_steps = np.linspace(start, start + 10, num_time_steps) #在[start,start+10]區間均勻地取num_points個點 57 data = np.sin(time_steps) 58 data = data.reshape(num_time_steps, 1) #[num_time_steps,]->[num_points,1] 59 x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) #輸入前49個點(seq_len=49)，即下標0~48[batch, seq_len, feature_len] 60 y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) #預測后49個點，即下標1~49 61 #以上步驟生成(x,y)數據對 62 63 output, hidden_prev = model(x, hidden_prev) #喂入模型得到輸出 64 hidden_prev = hidden_prev.detach() 65 66 loss = criterion(output, y) #計算MSE損失 67 model.zero_grad() 68 loss.backward() 69 optimizer.step() 70 71 if iter % 1000 == 0: 72 print("Iteration: {} loss {}".format(iter, loss.item())) 73 74 75 #測試過程 76 #先用同樣的方式生成一組數據x,y 77 start = np.random.randint(3, size=1)[0] 78 time_steps = np.linspace(start, start + 10, num_time_steps) 79 data = np.sin(time_steps) 80 data = data.reshape(num_time_steps, 1) 81 x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) 82 y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) 83 84 predictions = [] 85 86 input = x[:, 0, :] #取seq_len里面第0號數據 87 input = input.view(1, 1, 1) #input：[1,1,1] 88 for _ in range(x.shape[1]): #迭代seq_len次 89 90 pred, hidden_prev = model(input, hidden_prev) 91 input = pred #預測出的(下一個點的)序列pred當成輸入(或者直接寫成input, hidden_prev = model(input, hidden_prev)) 92 predictions.append(pred.detach().numpy().ravel()[0]) 93 94 95 x = x.data.numpy() 96 y = y.data.numpy() 97 plt.plot(time_steps[:-1], x.ravel()) 98 99 plt.scatter(time_steps[:-1], x.ravel(), c='r') #x值 100 plt.scatter(time_steps[1:], y.ravel(), c='y') #y值 101 plt.scatter(time_steps[1:], predictions, c='b') #y的預測值 102 plt.show()
Iteration: 0 loss 0.4788994789123535
Iteration: 1000 loss 0.0007066279067657888
Iteration: 2000 loss 0.0002824284601956606
Iteration: 3000 loss 0.0006475357222370803
Iteration: 4000 loss 0.00019797398999799043
Iteration: 5000 loss 0.00011313191498629749
3.梯度裁剪
如果發生梯度爆炸，在上面67~69行之間要進行梯度裁剪：
1 model.zero_grad() 2 loss.backward() 3 for p in model.parameters(): 4 # print(p.grad.norm()) #查看參數p的梯度 5 torch.nn.utils.clip_grad_norm_(p, 10) #將梯度裁剪到小於10 6 optimizer.step()