非线性函数拟合

2023-12-28 03:57| 来源: 网络整理| 查看: 265

本次的目的是利用PB神经网络拟合非线性函数：y=x^2+x+1

导入相关库： import torch import torch.nn as nn from torch.optim import SGD import torch.utils.data as Data from sklearn.datasets import load_boston import pandas as pd import numpy as np import matplotlib.pyplot as plt from torchviz import make_dot from sklearn.preprocessing import StandardScaler, MinMaxScaler from sklearn.model_selection import train_test_split import hiddenlayer as hl from sklearn.metrics import accuracy_score,confusion_matrix,classification_report 手动生成数据集

既简单的生成x系列，并得到y

num = 400 train_x = torch.arange(-10, 10, 0.05) train_x = train_x.numpy() train_y = train_x * train_x + 2 * train_x + 1 train_x = train_x.reshape(num, 1) train_y = train_y.reshape(num,)

得到从-10到10的间隔为0.05的400个点，并得到了相关的因变量

为了适应神经网络的输入层，利用.reshape()将数据转置;

拆分训练集，测试集 X_train, X_test, y_train, y_test = train_test_split( train_x, train_y, test_size=0.1, random_state=123 )

test_size表示测试集的比率

random_state表示随机种子，可以在后期应用相同的随机分布

转换为张量，并生成数据集合

将数据都转换为数据类型为float32的张量

利用dateloder生成一个batch为360组数据的数据组

X_train_s = torch.from_numpy(X_train_s.astype(np.float32)) y_train = torch.from_numpy(y_train.astype(np.float32)) X_test_s = torch.from_numpy(X_test_s.astype(np.float32)) y_test = torch.from_numpy(y_test.astype(np.float32)) train_data = Data.TensorDataset(X_train_s, y_train) test_data = Data.TensorDataset(X_test_s,y_test) train_loader = Data.DataLoader( dataset=train_data, ## 使用的数据集 batch_size=360 # shuffle=True, # 每次迭代前打乱数据 # num_workers=1, # 使用两个进程 ) test_loader = Data.DataLoader( dataset=test_data, ## 使用的数据集 batch_size=len(test_data) # shuffle=True, # 每次迭代前打乱数据 # num_workers=1, # 使用两个进程 ) 定义网络：

共四层全连接层

class MLPmodel(nn.Module): def __init__(self): super(MLPmodel, self).__init__() ## 定义第一个隐藏层 self.hidden1 = nn.Linear(1, 200, bias=True) self.active1 = nn.ReLU() ## 定义第一个隐藏层 self.hidden2 = nn.Linear(200, 80) self.active2 = nn.ReLU() ## 定义预测回归层 self.hidden3 = nn.Linear(80,10) self.active3 = nn.ReLU() self.regression = nn.Linear(10, 1) ## 定义网络的向前传播路径 def forward(self, x): x = self.hidden1(x) x = self.active1(x) x = self.hidden2(x) x = self.active2(x) x = self.hidden3(x) x = self.active3(x) output = self.regression(x) ## 输出为output return output

网络结构为：

MLPmodel( (hidden1): Linear(in_features=1, out_features=200, bias=True) (active1): ReLU() (hidden2): Linear(in_features=200, out_features=80, bias=True) (active2): ReLU() (hidden3): Linear(in_features=80, out_features=10, bias=True) (active3): ReLU() (regression): Linear(in_features=10, out_features=1, bias=True) )

也可以采用相关库得到网络图：

x = torch.randn(1, 1, 50, 1).requires_grad_(True) y = mlp1(x) MyConvnetis = make_dot(y, params=dict(list(mlp1.named_parameters()) + [('x', x)])) MyConvnetis.format = "png" MyConvnetis.directory = r"C:\Users\12860\Desktop\2.png" MyConvnetis.view()

训练前的设置： mlp1 = MLPmodel() optimizer = torch.optim.Adam(mlp1.parameters(), lr=0.001) loss_func = nn.MSELoss() # 最小平方根误差 train_loss_all = [] ## 输出每个批次训练的损失函数 ## 进行训练，并输出每次迭代的损失函数 history1 = hl.History() # 使用Canvas进行可视化 canvas1 = hl.Canvas() print_step = 100 训练网络 for epoch in range(2000): ## 对训练数据的迭代器进行迭代计算 for step, (b_x, b_y) in enumerate(train_loader): output = mlp1(b_x).flatten() # MLP在训练batch上的输出 train_loss = loss_func(output, b_y) # 平方根误差 optimizer.zero_grad() # 每个迭代步的梯度初始化为0 train_loss.backward() # 损失的后向传播，计算梯度 optimizer.step() # 使用梯度进行优化 train_loss_all.append(train_loss.item()) niter = epoch*len(train_loader)+step+1 if niter % print_step == 0: output1 = mlp1(X_test_s) # 为history添加epoch，损失和精度 y_test=y_test.reshape(len(y_test),1) test_loss = loss_func(output1,y_test) history1.log(niter, test_loss=test_loss ) # 使用两个图像可视化损失函数和精度 with canvas1: canvas1.draw_plot(history1["test_loss"]) plt.figure() plt.plot(train_loss_all, "r-") plt.title("Train loss per iteration") plt.show() 利用hiddenlayer库进行可视化，test_loss图像是可以实时显示的：

验证网络 x1 = np.arange(-14, 14, 0.5) x1 = x1.reshape(len(x1), 1) y1 = x1* x1 + 2 * x1 + 1 #x1 = scales.fit_transform(x1) #y1 = scales.fit_transform(y1) plt.figure(2) plt.plot(x1, y1, 'r-') x2 = np.arange(-14, 14, 0.5) x2 = x2.reshape(len(x2), 1) #x2 = scales.transform(x2) x2 = torch.from_numpy(x2.astype(np.float32)) y2 = mlp1(x2) x2 = x2.numpy() y2 = y2.detach().numpy() plt.scatter(x2, y2) plt.show()

拟合效果在训练集附近比较准确，原理训练集之后会慢慢降低准确度。

总体代码： import torch import torch.nn as nn from torch.optim import SGD import torch.utils.data as Data from sklearn.datasets import load_boston import pandas as pd import numpy as np import matplotlib.pyplot as plt from torchviz import make_dot from sklearn.preprocessing import StandardScaler, MinMaxScaler from sklearn.model_selection import train_test_split import hiddenlayer as hl from sklearn.metrics import accuracy_score,confusion_matrix,classification_report num = 400 train_x = torch.arange(-10, 10, 0.05) train_x = train_x.numpy() train_y = train_x * train_x + 2 * train_x + 1 train_x = train_x.reshape(num, 1) train_y = train_y.reshape(num,) X_train, X_test, y_train, y_test = train_test_split( train_x, train_y, test_size=0.1, random_state=123 ) scales = MinMaxScaler(feature_range=(0, 1)) X_train_s= X_train X_test_s=X_test X_train_s = torch.from_numpy(X_train_s.astype(np.float32)) y_train = torch.from_numpy(y_train.astype(np.float32)) X_test_s = torch.from_numpy(X_test_s.astype(np.float32)) y_test = torch.from_numpy(y_test.astype(np.float32)) train_data = Data.TensorDataset(X_train_s, y_train) test_data = Data.TensorDataset(X_test_s,y_test) train_loader = Data.DataLoader( dataset=train_data, ## 使用的数据集 batch_size=360 # shuffle=True, # 每次迭代前打乱数据 # num_workers=1, # 使用两个进程 ) test_loader = Data.DataLoader( dataset=test_data, ## 使用的数据集 batch_size=len(test_data) # shuffle=True, # 每次迭代前打乱数据 # num_workers=1, # 使用两个进程 ) class MLPmodel(nn.Module): def __init__(self): super(MLPmodel, self).__init__() ## 定义第一个隐藏层 self.hidden1 = nn.Linear(1, 200, bias=True) self.active1 = nn.ReLU() ## 定义第一个隐藏层 self.hidden2 = nn.Linear(200, 80) self.active2 = nn.ReLU() ## 定义预测回归层 self.hidden3 = nn.Linear(80,10) self.active3 = nn.ReLU() self.regression = nn.Linear(10, 1) ## 定义网络的向前传播路径 def forward(self, x): x = self.hidden1(x) x = self.active1(x) x = self.hidden2(x) x = self.active2(x) x = self.hidden3(x) x = self.active3(x) output = self.regression(x) ## 输出为output return output ## 输出我们的网络结构 mlp1 = MLPmodel() optimizer = torch.optim.Adam(mlp1.parameters(), lr=0.001) loss_func = nn.MSELoss() # 最小平方根误差 train_loss_all = [] ## 输出每个批次训练的损失函数 ## 进行训练，并输出每次迭代的损失函数 history1 = hl.History() # 使用Canvas进行可视化 canvas1 = hl.Canvas() print_step = 100 for epoch in range(2000): ## 对训练数据的迭代器进行迭代计算 for step, (b_x, b_y) in enumerate(train_loader): output = mlp1(b_x).flatten() # MLP在训练batch上的输出 train_loss = loss_func(output, b_y) # 平方根误差 optimizer.zero_grad() # 每个迭代步的梯度初始化为0 train_loss.backward() # 损失的后向传播，计算梯度 optimizer.step() # 使用梯度进行优化 train_loss_all.append(train_loss.item()) niter = epoch*len(train_loader)+step+1 if niter % print_step == 0: output1 = mlp1(X_test_s) # 为history添加epoch，损失和精度 y_test=y_test.reshape(len(y_test),1) test_loss = loss_func(output1,y_test) history1.log(niter, test_loss=test_loss ) # 使用两个图像可视化损失函数和精度 with canvas1: canvas1.draw_plot(history1["test_loss"]) x = torch.randn(1, 1, 50, 1).requires_grad_(True) y = mlp1(x) MyConvnetis = make_dot(y, params=dict(list(mlp1.named_parameters()) + [('x', x)])) MyConvnetis.format = "png" MyConvnetis.directory = r"C:\Users\12860\Desktop\2.png" MyConvnetis.view() plt.figure() plt.plot(train_loss_all, "r-") plt.title("Train loss per iteration") plt.show() x1 = np.arange(-14, 14, 0.5) x1 = x1.reshape(len(x1), 1) y1 = x1* x1 + 2 * x1 + 1 #x1 = scales.fit_transform(x1) #y1 = scales.fit_transform(y1) plt.figure(2) plt.plot(x1, y1, 'r-') x2 = np.arange(-14, 14, 0.5) x2 = x2.reshape(len(x2), 1) #x2 = scales.transform(x2) x2 = torch.from_numpy(x2.astype(np.float32)) y2 = mlp1(x2) x2 = x2.numpy() y2 = y2.detach().numpy() plt.scatter(x2, y2) plt.show()

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非线性函数拟合

非线性函数拟合

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