请用python写一个3*4*5*1的bp神经网络模型

以下为Python代码实现一个3*4*5*1的BP神经网络模型：

import numpy as np

class NeuralNetwork:
    def __init__(self):
        np.random.seed(1)
        self.weights = [np.random.randn(4, 3), np.random.randn(5, 4), np.random.randn(1, 5)]
        self.biases = [np.zeros((4, 1)), np.zeros((5, 1)), np.zeros((1, 1))]

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

    def sigmoid_derivative(self, z):
        return self.sigmoid(z) * (1 - self.sigmoid(z))

    def forward(self, X):
        Z1 = np.dot(self.weights[0], X) + self.biases[0]
        A1 = self.sigmoid(Z1)
        Z2 = np.dot(self.weights[1], A1) + self.biases[1]
        A2 = self.sigmoid(Z2)
        Z3 = np.dot(self.weights[2], A2) + self.biases[2]
        A3 = self.sigmoid(Z3)

        return A3

    def train(self, X, Y, epochs, learning_rate):
        for epoch in range(epochs):
            for i in range(len(X)):
                a = X[i].reshape(-1, 1)
                y = Y[i]

                Z1 = np.dot(self.weights[0], a) + self.biases[0]
                A1 = self.sigmoid(Z1)
                Z2 = np.dot(self.weights[1], A1) + self.biases[1]
                A2 = self.sigmoid(Z2)
                Z3 = np.dot(self.weights[2], A2) + self.biases[2]
                A3 = self.sigmoid(Z3)

                error = A3 - y
                dZ3 = error * self.sigmoid_derivative(Z3)
                dW3 = np.dot(dZ3, A2.T)
                dB3 = dZ3
                dZ2 = np.dot(self.weights[2].T, dZ3) * self.sigmoid_derivative(Z2)
                dW2 = np.dot(dZ2, A1.T)
                dB2 = dZ2
                dZ1 = np.dot(self.weights[1].T, dZ2) * self.sigmoid_derivative(Z1)
                dW1 = np.dot(dZ1, a.T)
                dB1 = dZ1

                self.weights[2] -= learning_rate * dW3
                self.biases[2] -= learning_rate * dB3
                self.weights[1] -= learning_rate * dW2
                self.biases[1] -= learning_rate * dB2
                self.weights[0] -= learning_rate * dW1
                self.biases[0] -= learning_rate * dB1

        print("Training completed!")

# Example usage:
X = np.random.randn(3, 4, 5, 1) # 3x4x5x1 input tensor
Y = np.random.randn(1, 1) # 1x1 expected output
model = NeuralNetwork()
model.train(X, Y, epochs=100, learning_rate=0.1)