[ot-users] Some doubts on Polynomial Chaos

Andrea TRUCCHIA trucchia at cerfacs.fr
Mon Dec 11 13:54:30 CET 2017

Dear User Community of OT, 

I am a researcher at CERFACS that is using OT as an important part of his PhD thesis. 

I have been trying to find a combinations of best procedures that would help me giving reasonably good results for a wide range of forest fire simulations, having 2 or 3 input parameters. 

The methods I have been using recently for the PC are 

- for the Truncature part of the algorithm, an ot.FixedStrategy() with linear EnumerateFunction(). I have planned to try some hyperbolic truncature as soon as possible. 

-for the ProjectionStrategy, aside from the quadrature method, that is quite expensive regarding the number of DOE points to be evaluated, I tried 

-- ot.LeastSquareStrategy(X,Y) , the default one that I imagine is a Penalized Least Square algorithm (but without explicitly setting a penalty parameter) 
-- ot.LeastSquareStrategy(X, Y, LeastSquaresMetaModelSelectionFactory (LARS(),CorrectedLeaveOneOut() ) 

The questions I have right now are 

1) Where can I find some documentation about the Penalized Least Square algorithm implemented in LeastSquareStrategy ? Is the penalty applied in the code related to the second derivatives of the response surface? 

2) Is the LARS() the most performant algorithm we have in PC right now, in the OpenTurns framework? Is there any difference between calling LAR() and LARS() ? Where can I find a documentation for the real "flavour" of the LARS() implemented? 

3) Where can I find some example of the implementation of an AdaptiveStrategy, in the form of a SequentialStrategy or CleaningStrategy ? Talkin about a wide range of applications, i.e. do not dealing with a specific problem, are they worth the effort of their implementation? 

Thanks in advance to anyone who will reply 

Best Regards 

Andrea Trucchia 
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