Applicability of learning

[Rac78]

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 2-3 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?

[yaser]

Originally Posted by Rac78

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 2-3 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?

Hi,

Interesting point. A couple of years ago, a colleague of mine at Caltech resorted to learning for precisely this reason.