cnn机器学习时python版本不兼容报错

在使用python执行CNN算法时，发生如下报错：

A module that was compiled using NumPy 1.x cannot be run in NumPy 2.1.1 as it may crash. 
To support both 1.x and 2.x versions of NumPy, modules must be compiled with NumPy 2.0. Some module may need to rebuild instead e.g. with 'pybind11>=2.12'. 

If you are a user of the module, the easiest solution will be to downgrade to 'numpy<2' or try to upgrade the affected module. 
We expect that some modules will need time to support NumPy 2.

这时候需要安装指定版本。

pip install numpy==1.26.4

安装完成后重新运行代码。

import tensorflow as tf
from keras import datasets, layers, models
import matplotlib.pyplot as plt

# 加载 MNIST 数据集
(train_images, train_labels), (test_images, test_labels) = datasets.mnist.load_data()
train_images, test_images = train_images / 255.0, test_images / 255.0
train_images = train_images.reshape((train_images.shape[0], 28, 28, 1))
test_images = test_images.reshape((test_images.shape[0], 28, 28, 1))

# 构建 CNN 模型
model = models.Sequential([
    layers.Conv2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)),
    layers.MaxPooling2D((2, 2)),
    layers.Conv2D(64, (3, 3), activation='relu'),
    layers.MaxPooling2D((2, 2)),
    layers.Conv2D(64, (3, 3), activation='relu'),
    layers.Flatten(),
    layers.Dense(64, activation='relu'),
    layers.Dense(10, activation='softmax')
])

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

# 训练模型
history = model.fit(train_images, train_labels, epochs=10, 
                    validation_data=(test_images, test_labels))

# 评估模型
test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2)
print(f'\nTest accuracy: {test_acc:.4f}')

# 绘制训练过程中的准确率
plt.figure(figsize=(12, 4))

plt.subplot(1, 2, 1)
plt.plot(history.history['accuracy'], label='Training Accuracy')
plt.plot(history.history['val_accuracy'], label='Validation Accuracy')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.legend()
plt.title('Accuracy Over Time')
plt.show()

成功运行得出结果。