Designing conservative surrogates with cross validation

[Felipe A. C. Viana]

Dear all,

Here it is a reference on how to build surrogates that are
conservative estimators of a function:

F.A.C. Viana, V. Picheny, and R.T. Haftka, "Using cross validation to
design conservative surrogates," AIAA Journal, Vol. 48 (10), pp.
2286-2298, 2010 (DOI: 10.2514/1.J050327).

The use of surrogates (also known as metamodels) for facilitating
optimization and statistical analysis of computationally expensive
simulations has become commonplace. Surrogate models are usually fit
to be unbiased (i.e., the error expectation is zero). However, in
certain applications, it might be important to safely estimate the
response (e.g., in structural analysis, the maximum stress must not be
underestimated in order to avoid failure). In this work we use safety
margins to conservatively compensate for fitting errors associated
with surrogates. We propose the use of cross validation for estimating
the required safety margin for a desired level of conservativeness
(percentage of safe predictions). The approach was tested on three
algebraic examples for two basic surrogates: namely, kriging and
polynomial response surface. For these examples we found that cross
validation is effective for selecting the safety margin. We also
applied the approach to the probabilistic design optimization of a
composite laminate. This design under uncertainty example showed that
the approach can be successfully used in engineering applications.

You can find more about it on:
http://sites.google.com/site/fchegury/publications

All the best,
Felipe A. C. Viana