请用TensorFlow2构建一个DCGAN模型生成数字图片，包括模型的搭建，编译及训练。

好的，我可以为您提供一个基于TensorFlow2的DCGAN模型生成数字图片的示例代码，包括模型的搭建、编译和训练过程。

首先，我们需要导入所需的库和模块：

import tensorflow as tf
from tensorflow.keras import layers
import numpy as np
import matplotlib.pyplot as plt

然后，我们需要定义生成器和判别器模型。生成器用于生成合成图像，判别器用于判断输入的图像是真实图像还是合成图像。

# 定义生成器模型
def make_generator_model():
    model = tf.keras.Sequential()
    model.add(layers.Dense(7*7*256, use_bias=False, input_shape=(100,)))
    model.add(layers.BatchNormalization())
    model.add(layers.LeakyReLU())

    model.add(layers.Reshape((7, 7, 256)))
    assert model.output_shape == (None, 7, 7, 256) # 注意：batch size 没有限制

    model.add(layers.Conv2DTranspose(128, (5, 5), strides=(1, 1), padding='same', use_bias=False))
    assert model.output_shape == (None, 7, 7, 128)
    model.add(layers.BatchNormalization())
    model.add(layers.LeakyReLU())

    model.add(layers.Conv2DTranspose(64, (5, 5), strides=(2, 2), padding='same', use_bias=False))
    assert model.output_shape == (None, 14, 14, 64)
    model.add(layers.BatchNormalization())
    model.add(layers.LeakyReLU())

    model.add(layers.Conv2DTranspose(1, (5, 5), strides=(2, 2), padding='same', use_bias=False, activation='tanh'))
    assert model.output_shape == (None, 28, 28, 1)

    return model

# 定义判别器模型
def make_discriminator_model():
    model = tf.keras.Sequential()
    model.add(layers.Conv2D(64, (5, 5), strides=(2, 2), padding='same',
                                     input_shape=[28, 28, 1]))
    model.add(layers.LeakyReLU())
    model.add(layers.Dropout(0.3))

    model.add(layers.Conv2D(128, (5, 5), strides=(2, 2), padding='same'))
    model.add(layers.LeakyReLU())
    model.add(layers.Dropout(0.3))

    model.add(layers.Flatten())
    model.add(layers.Dense(1))

    return model

接下来，我们需要定义损失函数、优化器和辅助函数：

# 定义损失函数
cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True)

# 定义生成器损失函数
def generator_loss(fake_output):
    return cross_entropy(tf.ones_like(fake_output), fake_output)

# 定义判别器损失函数
def discriminator_loss(real_output, fake_output):
    real_loss = cross_entropy(tf.ones_like(real_output), real_output)
    fake_loss = cross_entropy(tf.zeros_like(fake_output), fake_output)
    total_loss = real_loss + fake_loss
    return total_loss

# 定义生成器和判别器优化器
generator_optimizer = tf.keras.optimizers.Adam(1e-4)
discriminator_optimizer = tf.keras.optimizers.Adam(1e-4)

# 定义辅助函数，用于生成一些噪声作为输入，并生成合成图像
def generate_and_save_images(model, epoch, test_input):
    # 生成图像
    predictions = model(test_input, training=False)

    # 绘制图像
    fig = plt.figure(figsize=(4, 4))
    for i in range(predictions.shape[0]):
        plt.subplot(4, 4, i+1)
        plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray')
        plt.axis('off')

    # 保存图像
    plt.savefig('image_at_epoch_{:04d}.png'.format(epoch))
    plt.show()

然后，我们需要定义训练过程：

# 定义训练过程
@tf.function
def train_step(images):
    noise = tf.random.normal([BATCH_SIZE, 100])

    with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:
        generated_images = generator(noise, training=True)

        real_output = discriminator(images, training=True)
        fake_output = discriminator(generated_images, training=True)

        gen_loss = generator_loss(fake_output)
        disc_loss = discriminator_loss(real_output, fake_output)

    gradients_of_generator = gen_tape.gradient(gen_loss, generator.trainable_variables)
    gradients_of_discriminator = disc_tape.gradient(disc_loss, discriminator.trainable_variables)

    generator_optimizer.apply_gradients(zip(gradients_of_generator, generator.trainable_variables))
    discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator, discriminator.trainable_variables))

接下来，我们需要加载数据集并进行训练：

# 加载数据集
(train_images, train_labels), (_, _) = tf.keras.datasets.mnist.load_data()
train_images = train_images.reshape(train_images.shape[0], 28, 28, 1).astype('float32')
train_images = (train_images - 127.5) / 127.5 # 将像素值归一化到 [-1, 1] 区间内
BUFFER_SIZE = 60000
BATCH_SIZE = 256
train_dataset = tf.data.Dataset.from_tensor_slices(train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE)

# 定义模型
generator = make_generator_model()
discriminator = make_discriminator_model()

# 训练模型
EPOCHS = 100
num_examples_to_generate = 16
noise_dim = 100

seed = tf.random.normal([num_examples_to_generate, noise_dim])

for epoch in range(EPOCHS):
    for image_batch in train_dataset:
        train_step(image_batch)

    # 生成一些图像并保存
    if epoch % 10 == 0:
        generate_and_save_images(generator, epoch, seed)

# 生成最终的一些图像并保存
generate_and_save_images(generator, EPOCHS, seed)

以上就是基于TensorFlow2的DCGAN模型生成数字图片的示例代码，包括模型的搭建、编译和训练过程。