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Robust calibration of numerical models based on relative regret

Victor Trappler 1 Élise Arnaud 1 Arthur Vidard 1 Laurent Debreu 1 
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Classical methods of calibration usually imply the minimisation of an objective function with respect to some control parameters. This function measures the error between some observations and the results obtained by a numerical model. In the presence of uncontrollable additional parameters that we model as random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced for such an optimisation problem.In this paper, we are going to present how to take into account those uncertainties by defining the relative-regret. This quantity allow us to compare the value of the objective function to its best performance achievable given a realisation of the random additional parameters. By controlling this relative-regret using a probabilistic constraint, we can then define a new family of estimators, whose robustness with respect to the random inputs can be adjusted.
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Victor Trappler, Élise Arnaud, Arthur Vidard, Laurent Debreu. Robust calibration of numerical models based on relative regret. Journal of Computational Physics, Elsevier, 2021, 426, pp.109952:1-19. ⟨10.1016/⟩. ⟨hal-02464780v3⟩



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