BP神经网络模型的代码

以下是一个简单的BP神经网络模型的Python代码，包括前向传播和反向传播：

import numpy as np

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size

        # 初始化权重和偏置
        self.weights_input_hidden = np.random.randn(self.input_size, self.hidden_size)
        self.bias_hidden = np.random.randn(self.hidden_size)
        self.weights_hidden_output = np.random.randn(self.hidden_size, self.output_size)
        self.bias_output = np.random.randn(self.output_size)

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def forward(self, inputs):
        # 前向传播
        hidden = self.sigmoid(np.dot(inputs, self.weights_input_hidden) + self.bias_hidden)
        output = self.sigmoid(np.dot(hidden, self.weights_hidden_output) + self.bias_output)
        return output

    def sigmoid_derivative(self, x):
        return x * (1 - x)

    def backward(self, inputs, targets, learning_rate):
        # 反向传播
        hidden = self.sigmoid(np.dot(inputs, self.weights_input_hidden) + self.bias_hidden)
        output = self.sigmoid(np.dot(hidden, self.weights_hidden_output) + self.bias_output)

        output_error = targets - output
        output_delta = output_error * self.sigmoid_derivative(output)

        hidden_error = np.dot(output_delta, self.weights_hidden_output.T)
        hidden_delta = hidden_error * self.sigmoid_derivative(hidden)

        self.weights_hidden_output += learning_rate * np.dot(hidden.T, output_delta)
        self.bias_output += learning_rate * np.sum(output_delta, axis=0)

        self.weights_input_hidden += learning_rate * np.dot(inputs.T, hidden_delta)
        self.bias_hidden += learning_rate * np.sum(hidden_delta, axis=0)

    def train(self, inputs, targets, num_epochs, learning_rate):
        for i in range(num_epochs):
            self.backward(inputs, targets, learning_rate)

    def predict(self, inputs):
        return self.forward(inputs)

使用方法：

# 创建神经网络模型
nn = NeuralNetwork(input_size=2, hidden_size=4, output_size=1)

# 训练模型
inputs = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
targets = np.array([[0], [1], [1], [0]])
nn.train(inputs, targets, num_epochs=10000, learning_rate=0.1)

# 预测
print(nn.predict(np.array([[0, 0], [0, 1], [1, 0], [1, 1]])))