Optimizing DL trained output function with optimization packages/frameworks

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I ask a question about optimizing the trained function of a PyTorch-written deep neural network (data-driven optimization) here, but it looks like there isn't any solution for it.

In my previous effort, I trained a DL networked in PyTorch, exported the output function using torch.jit.trace, and tried to optimize the trained output function with Pyomo, But it didn't work.

Now, I want to ask what other alternative framework combination (DL framework + optimization framework) can I use to first train my network and then optimize the output trained function without any problem?

It should be noted that my training data are some physical properties (such as temperature, pressure, etc.) therefore I am facing a regression problem.

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