Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification

Algorithms

TimJ. Sullivan¹  Éric Savin²  Luc Bonnet²  Jean-Luc Akian² 

[1] Mathematics Institute and School of Engineering, University of Warwick, Coventry CV4 7AL, UK;ONERA, 29 Avenue de la Division Leclerc, 92320 Châtillon, France;

关键词: adaptive approximation;    isotonic regression;    optimisation under uncertainty;    uncertainty quantification;    aerodynamic design;   

DOI  :  10.3390/a13080196

来源: DOAJ

【 摘 要 】

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.

【 授权许可】

Unknown