Applicability of learning
In lectures 1 and 2 (and HW1), it was mentioned several times that learning from data is not ideal for situations where we already have an analytical model. I wonder if there are times when learning may help.
Suppose I have a large multiphysics code that takes a long time to run. For instance, a runtime for a typical case may take 23 days, and if I am interested in running 10000 cases, running the code isn't feasible. Can learning helps to generate an approximation to the code (perhaps with an applicability limited to a small subset of the valid input space). The data could come from past validation tests and maybe a more limited number of code runs. (Let's assume that simplifying the underlying equations to improve runtime isn't practical.) Are there learning models where, if we know the underlying equations/correlations, this knowledge can help with the learning? Once we have learned the problem, is it foreseeable that running that problem will be quicker than running the original code?
