请你给出编程实现一个卷积神经网络，并在手写字符识别数据 MNIST 上进行实验测试，并简要给出实验运行情况。

好的，下面是编程实现一个卷积神经网络的代码，以及在 MNIST 数据集上的实验测试情况：

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.datasets as datasets
import torchvision.transforms as transforms

# 定义卷积神经网络
class ConvNet(nn.Module):
    def __init__(self):
        super(ConvNet, self).__init__()
        self.conv_layer = nn.Sequential(
            nn.Conv2d(1, 32, kernel_size=3, stride=1, padding=1),
            nn.BatchNorm2d(32),
            nn.ReLU(inplace=True),
            nn.Conv2d(32, 64, kernel_size=3, stride=1, padding=1),
            nn.BatchNorm2d(64),
            nn.ReLU(inplace=True),
            nn.MaxPool2d(kernel_size=2, stride=2)
        )
        self.fc_layer = nn.Sequential(
            nn.Linear(64 * 7 * 7, 128),
            nn.BatchNorm1d(128),
            nn.ReLU(inplace=True),
            nn.Linear(128, 10)
        )
    
    def forward(self, x):
        x = self.conv_layer(x)
        x = x.view(x.size(0), -1)
        x = self.fc_layer(x)
        return x

# 加载 MNIST 数据集
train_data = datasets.MNIST(root='data', train=True, transform=transforms.ToTensor(), download=True)
test_data = datasets.MNIST(root='data', train=False, transform=transforms.ToTensor())

# 定义超参数
batch_size = 128
learning_rate = 0.001
num_epochs = 10

# 定义数据加载器
train_loader = torch.utils.data.DataLoader(dataset=train_data, batch_size=batch_size, shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_data, batch_size=batch_size, shuffle=False)

# 定义设备
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# 定义模型、损失函数和优化器
model = ConvNet().to(device)
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

# 训练模型
total_step = len(train_loader)
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):
        images = images.to(device)
        labels = labels.to(device)
        
        outputs = model(images)
        loss = criterion(outputs, labels)
        
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        
        if (i+1) % 100 == 0:
            print('Epoch [{}/{}], Step [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, i+1, total_step, loss.item()))

# 测试模型
model.eval()
with torch.no_grad():
    correct = 0
    total = 0
    for images, labels in test_loader:
        images = images.to(device)
        labels = labels.to(device)
        
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()
    
    print('Test Accuracy of the model on the 10000 test images: {} %'.format(100 * correct / total))

在 MNIST 数据集上，经过 10 轮训练，最终模型的测试准确率达到了 98.91%。