After trying again and again, I finally found the problem. Let me briefly describe the prerequisites and solutions.
Prerequisites

The model parameter type is Double
The input parameter is also of type Double
Therefore, the model saved by torch::save is also of Double type

Solutions
After LibTorch saves the model, before loading the model, the network needs to be initialized first. If you want to read an offline network file of type Double, you must first initialize the network to type Double, then load the model from file, which is very, very important. The sample code is shown below.
// Initialize the network
Net model = Net(in_feature, out_feature);
model->to(device, torch::kDouble);
// some code to train and validate and more...
torch::save(model, "test.pt");

// Load the model
Net new_model = Net(in_feature, out_feature);
new_model->to(device, torch::kDouble); // very very important before load
torch::load(new_model, "test.pt");

In summary, whether it is to save the model or load the model, the data type must be consistent throughout the process.
Thank you very much for all your suggestions and help!
Have a good day!