Questions for choosing model for History Matching

Since I am working on a project about Automated History Matching Project in Petroleum. For those who doesn’t know about that, it’s basically that I have a bunch of data of real production rate of oil, gas, water, etc… I know theoretical function to calculate those value and it should be fitted around 70-80% with the real data, and regularly the paramaters in those functions should be tuned by hand (as those params are all uncertainties so even when we survey stuff, no value are 100% the right one), but now I want to build a deep model that can choose params to calculate and fit the results with real data, output should be those params.

I am currently consider using Physics Informed Neural Network, or Reforcement Learning. But it seems so difficult to figure out what is the suitable one for this. I need helps from you guys. Thank you for spending time reading this.

If this is a time-series situation (i.e. predicting variations in production over time), I’d guess that a recurrent neural network (i.e. a sequence model) would be useful.