neuraloperator/physics_informed ? reverse-engineered prompt

Build me a working Python project for physics informed neural operator experiments that can train, evaluate, and fine tune models for PDE problems like Burgers, Darcy flow, and Navier Stokes.

I want a simple setup where I can download or prepare the example data, run training from config files, test a trained model, and do inference or instance level optimization on a chosen sample range. It should include the main model options from the project, plus the baseline methods like DeepONet and PINN style training, so I can compare results easily.

Please make the scripts easy to run from the command line, with clear defaults, sensible folder organization, and helpful error messages if data or dependencies are missing. If anything needs current library versions or docs, look them up online first. I also want the README to explain the basic workflow in plain language, including how to train, evaluate, and run the demo cases.