bp神经网络回归python源码

以下是一个使用BP神经网络进行回归的Python源码示例：

import numpy as np
import matplotlib.pyplot as plt

# 定义BP神经网络类
class BPNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        # 随机初始化权重
        self.weights_ih = np.random.randn(hidden_size, input_size)
        self.weights_ho = np.random.randn(output_size, hidden_size)
        self.bias_h = np.random.randn(hidden_size, 1)
        self.bias_o = np.random.randn(output_size, 1)
        
    # 定义sigmoid激活函数
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    # 定义前向传播函数
    def forward(self, inputs):
        hidden = self.sigmoid(self.weights_ih @ inputs + self.bias_h)
        output = self.sigmoid(self.weights_ho @ hidden + self.bias_o)
        return output
    
    # 定义反向传播函数
    def backward(self, inputs, targets, learning_rate):
        # 前向传播
        hidden = self.sigmoid(self.weights_ih @ inputs + self.bias_h)
        output = self.sigmoid(self.weights_ho @ hidden + self.bias_o)
        
        # 计算误差
        error = targets - output
        
        # 更新权重和偏置
        gradient_output = output * (1 - output) * error
        gradient_hidden = hidden * (1 - hidden) * (self.weights_ho.T @ gradient_output)
        
        self.weights_ho += learning_rate * gradient_output @ hidden.T
        self.weights_ih += learning_rate * gradient_hidden @ inputs.T
        self.bias_o += learning_rate * gradient_output
        self.bias_h += learning_rate * gradient_hidden
        
    # 定义训练函数
    def train(self, inputs, targets, epochs, learning_rate):
        for i in range(epochs):
            for j in range(len(inputs)):
                self.backward(inputs[j], targets[j], learning_rate)
                
    # 定义预测函数
    def predict(self, inputs):
        return self.forward(inputs)

# 示例用法
inputs = np.array([[0], [1], [2], [3], [4], [5]])
targets = np.array([[0], [1], [4], [9], [16], [25]])

# 创建BP神经网络对象
network = BPNeuralNetwork(input_size=1, hidden_size=4, output_size=1)

# 训练网络
network.train(inputs, targets, epochs=10000, learning_rate=0.1)

# 预测并打印结果
for input in inputs:
    output = network.predict(input)
    print(f"Input: {input}, Predicted Output: {output}")

# 绘制拟合曲线
plt.plot(inputs, targets, 'ro', label='True')
plt.plot(inputs, [network.predict(input) for input in inputs], label='Predicted')
plt.legend()
plt.show()

这段代码实现了一个简单的BP神经网络进行回归的例子。首先定义了一个BPNeuralNetwork类，其中包括初始化权重、定义激活函数、前向传播函数、反向传播函数、训练函数和预测函数等方法。接下来创建了一个示例输入和目标输出，然后创建一个BP神经网络对象并对其进行训练。最后使用训练好的神经网络进行预测，并绘制出拟合曲线。