The OQUAIDOa applied mathematics chair, launched in January 2016 and hosted by the École des Mines engineering school in Saint-Étienne, brings together academic and industrial partnersb to tackle questions relating to the use of numerical simulators, such as uncertainty quantification, inversion and optimization. Its objective is to work on “upstream” research problems guided by practical applications.

A thesis(1) was carried out within the framework of this chair under the supervision of the Grenoble Alpes University, the École Centrale de Lyon and IFPEN. The application objective was to define the parameters for a vehicle pollution control system in order to comply with pollutant gas emission standards.

Of the many sources of uncertainty relating to the control of this system, the one that has the greatest impact is the variability of the driving cycle in real conditions. Hence in practice, compliance with standards is achieved by averaging, for a given sample of cycles, emission values estimated by a numerical simulator (figure).

Respect de la norme
For two control parameters, estimation (in green) of the NH3 emission standard compliance set (initial simulated points in black, points added via the iterative method in red).

Simulation calculation time was thus reduced, using an approximation of the simulator via a Gaussian process and a dimension reduction applied to the
functional variable. Combining these techniques with an iterative uncertainty reduction method not only considerably reduced the number of required
simulations, compared with state-of-the art methods, but it also made it possible to control estimation errors of the admissible set for the control system

a - From the French “Optimisation et QUAntification d'Incertitudes pour les Données Onéreuses”.

b - BRGM, CEA, CNRS, École Centrale de Lyon, IFPEN, IRSN, École des Mines engineering school in Saint-Étienne, Safran, Storengy, Grenoble-Alpes University, Nice Sophia Antipolis University, Toulouse Paul Sabathier University.

(1) M. R. El Amri, Uncertainty and robustness analysis for functional input and output models, Grenoble Alpes University PhD thesis, defended in 2019.

(2) M. R. El Amri, C. Helbert, O. Lepreux, M. Munoz Zuniga, C. Prieur, D. Sinoquet, Data-driven stochastic inversion under functional uncertainties, Statistics and Computing journal, 2019 Sept.

Scientific contact: Delphine Sinoquet




Research engineer / project leader in optimization
PhD in applied mathematics