Local optimization of black-box functions with high or infinite-dimensional inputs: application to nuclear safety

Abstract

International audienceBlack-box optimization problems when the input space is a high-dimensional space or a function space appear in more and more applications. In this context, the methods available for finite-dimensional data do not apply. The aim is then to propose a general method for optimization involving dimension reduction techniques. Different dimension reduction basis are considered (including data-driven basis). The methodology is illustrated on simulated functional data. The choice of the different parameters, in particular the dimension of the approximation space, is discussed. The method is finally applied to a problem of nuclear safety

Optimal designs for experiments for scalar-on-function linear models

“…Statistical modelling with functional data is well established in the statistics literature, see Ramsay and Silverman (1997) and Ramsay and Silverman (2005) for an introduction. However, the design of experiments for such models has received much less attention, with two main approaches being proposed: response surface methods using dimension-reduction techniques (Georgakis 2013, Roche 2015, Roche 2018and Klebanov and Georgakis 2016 and optimal design for dynamic models, typically derived from differential equations (Balsa-Canto andBanga 2007 andUciński andBogacka 2007). We develop methodology related to the response surface approach to find optimal functions for profile variables assuming a scalar-on-function linear model.…”

Lasso in infinite dimension: application to variable selection in functional multivariate linear regression

“…This is the case in Aneiros-Pérez et al (2004) where the aim is to predict ozone concentration of the day after from ozone concentration curve, N O concentration curve, N O 2 concentration curve, wind speed curve and wind direction of the current day. Another example comes from nuclear safety problems where we study the risk of failure of a nuclear reactor vessel in case of loss of coolant accident as a function of the evolution of temperature, pressure and heat transfer parameter in the vessel (Roche, 2018). The aim of the article is to study the link between a real response Y and a vector of covariates X = (X 1 , ..., X p ) with observations {(Y i , X i ), i = 1, ..., n} where X i = (X 1 i , ..., X p i ) is a vector of covariates which can be of different nature (curves or vectors).…”