请用python编写一个识别手写数字的神经网络程序

在Python中，我们可以使用深度学习库Keras或TensorFlow来创建一个简单的卷积神经网络（Convolutional Neural Network, CNN），用于识别MNIST数据集中的手写数字。以下是一个简化的示例，使用Keras：

import keras
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers import Dense, Conv2D, Flatten

# 加载MNIST数据
(x_train, y_train), (x_test, y_test) = mnist.load_data()

# 数据预处理
x_train = x_train.reshape(-1, 28, 28, 1)
x_test = x_test.reshape(-1, 28, 28, 1)
x_train, x_test = x_train / 255.0, x_test / 255.0
y_train = keras.utils.to_categorical(y_train, 10)
y_test = keras.utils.to_categorical(y_test, 10)

# 创建模型
model = Sequential([
    Conv2D(32, kernel_size=(3, 3), activation='relu', input_shape=(28, 28, 1)),
    MaxPooling2D(pool_size=(2, 2)),
    Conv2D(64, kernel_size=(3, 3), activation='relu'),
    MaxPooling2D(pool_size=(2, 2)),
    Flatten(),
    Dense(128, activation='relu'),
    Dense(10, activation='softmax')  # 输出层，10个节点对应10个类别
])

# 编译模型
model.compile(optimizer='adam',
              loss='categorical_crossentropy',
              metrics=['accuracy'])

# 训练模型
model.fit(x_train, y_train, epochs=10, validation_data=(x_test, y_test))

# 测试模型
test_loss, test_acc = model.evaluate(x_test, y_test)
print(f"Test accuracy: {test_acc}")