Speaker
Description
Quantification of all sources of uncertainties when modeling a physical system is essential to build an accurate digital twin and make informed decisions in an operational situation [1]. In uncertainty quantification of numerical simulation models, the classical approach for estimating distribution function or quantile function of a model output variable requires availability of an entire sample of the studied variable (i.e. the outputs of all the simulation model runs) [2]. This approach is not suitable at exascale as large ensembles of simulation runs would need to gather and store a prohibitively large amount of data [3]. For quantile estimation, this problem can be solved thanks to an on-the-fly (also called iterative or recursive) approach based on the Robbins-Monro algorithm [4]. An algorithm has been proposed for quantile function estimation in the context of uncertainty quantification [5]: it aims to estimate quantiles (at orders ranging from 5% to 95%) from samples of limited size (a few hundred observations). We illustrate it on toy functions and real application cases. We also provide some implementation elements inside the python package ‘IterativeStatistics’ [6] (which includes other statistics as mean, variance, covariance and first-order Sobol’ index). This package is integrated into the Melissa system (on-line processing of data produced from large scale ensemble runs [7,8]) and will be also integrated into the SALOME platform [9] soon.
[1] A. Thelen, X. Zhang, O. Fink, Y. Lu, S. Ghosh, B.D. Youn, M.D. Todd, S. Mahadevan, C. Hu, Z. Hu. A comprehensive review of digital twin—part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives. Structural and Multidisciplinary Optimization, 66 (1), 2023.
[2] R. Smith. Uncertainty quantification, SIAM, 2014.
[3] A. Ribés, T. Terraz, Y. Fournier, B. Iooss and B. Raffin. Unlocking large scale uncertainty quantification with in-transit iterative statistics, In: In situ visualization for computational science, H. Childs, J. Bennet and C. Garth (Eds), Springer, 2022.
[4] Robbins, H. and S. Monro. A stochastic approximation method. The Annals of Mathematical Statistics 22, 400–407, 1951.
[5] B. Iooss and J. Lonchampt. Robust tuning of Robbins-Monro algorithm for iterative uncertainty quantification - Application to wind-farm asset management, Proceedings of the 31st European Safety and Reliability Conference, B. Castanier, M. Cepin, D. Bigaud and C. Berenguer (Eds.), Research Publishing, Singapore, 2021. Conference ESREL 2021, Angers, France, September 2021.
[6] https://pypi.org/project/iterative-stats/
[7] T. Terraz, A. Ribés, Y. Fournier, B. Iooss and B. Raffin. Large scale in transit global sensitivity analysis avoiding intermediate files, SC17 (The International Conference for High Performance Computing, Networking, Storage and Analysis), November 2017
[8] https://gitlab.inria.fr/melissa
[9] https://www.salome-platform.org/?lang=fr