写出关于bp神经网络模型的python代码

以下是一个简单的 BP 神经网络模型的 Python 代码：

import numpy as np

class BPNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 初始化权重矩阵和偏差向量
        self.weights1 = np.random.randn(self.input_size, self.hidden_size)
        self.bias1 = np.random.randn(self.hidden_size)
        self.weights2 = np.random.randn(self.hidden_size, self.output_size)
        self.bias2 = np.random.randn(self.output_size)
        
        # 定义激活函数
        self.activation_func = lambda x: 1 / (1 + np.exp(-x))
    
    def forward(self, X):
        # 前向传播计算输出值
        self.hidden_layer = self.activation_func(np.dot(X, self.weights1) + self.bias1)
        self.output_layer = self.activation_func(np.dot(self.hidden_layer, self.weights2) + self.bias2)
        return self.output_layer
    
    def backward(self, X, y, learning_rate):
        # 反向传播计算梯度并更新权重和偏差
        error = y - self.output_layer
        output_delta = error * self.output_layer * (1 - self.output_layer)
        hidden_error = np.dot(output_delta, self.weights2.T)
        hidden_delta = hidden_error * self.hidden_layer * (1 - self.hidden_layer)
        
        self.weights2 += learning_rate * np.dot(self.hidden_layer.T, output_delta)
        self.bias2 += learning_rate * np.sum(output_delta, axis=0)
        self.weights1 += learning_rate * np.dot(X.T, hidden_delta)
        self.bias1 += learning_rate * np.sum(hidden_delta, axis=0)
    
    def train(self, X, y, epochs, learning_rate):
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, learning_rate)
            loss = np.mean(np.square(y - output))
            if i % 100 == 0:
                print("Epoch: {0}, Loss: {1:.4f}".format(i, loss))
    
    def predict(self, X):
        return np.round(self.forward(X))

这个模型的输入是 `input_size` 维的特征向量，输出是 `output_size` 维的预测向量。隐藏层的大小为 `hidden_size`。在初始化时，权重和偏差向量都被随机初始化。前向传播使用 sigmoid 激活函数，反向传播使用梯度下降算法来更新权重和偏差。 `train` 方法用于训练模型， `predict` 方法用于对新的数据进行预测。