1.单步预测模型
%matplotlib inline
import torch
from torch import nn
from d2l import torch as d2l###############################################################################################################
# 初始化网络权重的函数
def init_weights(m):if type(m) == nn.Linear:nn.init.xavier_uniform_(m.weight)# 一个简单的多层感知机mlp
def get_net():net = nn.Sequential(nn.Linear(4, 10),nn.ReLU(),nn.Linear(10, 1))net.apply(init_weights)return net
def train(net, train_iter, loss, epochs, lr):trainer = torch.optim.Adam(net.parameters(), lr)for epoch in range(epochs):for X, y in train_iter:trainer.zero_grad()l = loss(net(X), y)l.sum().backward()trainer.step()print(f'epoch {epoch + 1}, 'f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')
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#准备数据集:生成一个sin的噪声函数:
T,tau =1000,4
time = torch.arange(1, T + 1, dtype=torch.float32)
x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))
features = torch.zeros((T - tau, tau))#训练数吃从第5个开始-1000个
for i in range(tau):features[:, i] = x[i: T - tau + i]
labels = x[tau:].reshape((-1, 1))
batch_size, n_train = 16, 600#600个样本用于训练(X1,X2,X3,X4) LABEL=X5
train_iter = d2l.load_array((features[:n_train], labels[:n_train]),batch_size, is_train=True)
net = get_net()
loss = nn.MSELoss(reduction='none')
train(net, train_iter, loss, 10, 0.01)
onestep_preds = net(features)
d2l.plot([time, time[tau:]],[x.detach().numpy(), onestep_preds.detach().numpy()], 'time','x', legend=['data', '1-step preds'], xlim=[1, 1000],figsize=(6, 3))
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2.多步预测模型
multistep_preds = torch.zeros(T)
multistep_preds[: n_train + tau] = x[: n_train + tau]
for i in range(n_train + tau, T):multistep_preds[i] = net(multistep_preds[i - tau:i].reshape((1, -1)))
d2l.plot([time, time[tau:], time[n_train + tau:]],[x.detach().numpy(), onestep_preds.detach().numpy(),multistep_preds[n_train + tau:].detach().numpy()], 'time','x', legend=['data', '1-step preds', 'multistep preds'],xlim=[1, 1000], figsize=(6, 3))
max_steps = 64
features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))
# 列i（i<tau）是来自x的观测，其时间步从（i）到（i+T-tau-max_steps+1）
for i in range(tau):features[:, i] = x[i: i + T - tau - max_steps + 1]# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i）到（i+T-tau-max_steps+1）
for i in range(tau, tau + max_steps):features[:, i] = net(features[:, i - tau:i]).reshape(-1)
steps = (1, 4, 16, 64)
d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],[features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],figsize=(6, 3))
