@ARTICLE
Matalon, P., Mycek, P., Ruede, U., Di Pietro, D.A., Hülsemann, F. and Ruiz, D. (2020) An h-Multigrid method for Hybrid High-Order discretizations
[bibtex]
@ARTICLE{AR-PA-20-136,
author = {Matalon, P. and Mycek, P. and Ruede, U. and Di Pietro, D.A. and Hülsemann, F. and Ruiz, D. },
title = {An h-Multigrid method for Hybrid High-Order discretizations},
year = {2020}}
Agullo, E., Altenbernd, M., Anzt, H., Bautista-Gomez, L.A., Benacchio, T., Bonaventura, L., Bungartz, H.J., Chatterjee, S., Ciorba, F.M., DeBardeleben, N., Drzisga, D., Eibl, S., Engelmann, C., Gansterer, W.N., Giraud, L., Göddeke, D., Heisig, M., Jézéquel, F., Kohl, N., Li, X.S., Lion, R., Mehl, M., Mycek, P., Obersteiner, M., Quintana-Orti, E.S., Rizzi, F., Ruede, U., Schulz, M., Fung, F., Speck, R., Stals, L., Teranishi, K., Thibault, S., Thönnes, D., Wagner, A. and Wohlmuth, B. (2020) Resiliency in Numerical Algorithm Design for Extreme Scale Simulations
[bibtex]
@ARTICLE{AR-PA-20-152,
author = {Agullo, E. and Altenbernd, M. and Anzt, H. and Bautista-Gomez, L.A. and Benacchio, T. and Bonaventura, L. and Bungartz, H.J. and Chatterjee, S. and Ciorba, F.M. and DeBardeleben, N. and Drzisga, D. and Eibl, S. and Engelmann, C. and Gansterer, W.N. and Giraud, L. and Göddeke, D. and Heisig, M. and Jézéquel, F. and Kohl, N. and Li, X.S. and Lion, R. and Mehl, M. and Mycek, P. and Obersteiner, M. and Quintana-Orti, E.S. and Rizzi, F. and Ruede, U. and Schulz, M. and Fung, F. and Speck, R. and Stals, L. and Teranishi, K. and Thibault, S. and Thönnes, D. and Wagner, A. and Wohlmuth, B. },
title = {Resiliency in Numerical Algorithm Design for Extreme Scale Simulations},
year = {2020}}
Mycek, P. and De Lozzo, M. (2019) Multilevel Monte Carlo Covariance Estimation for the Computation of Sobol' Indices, SIAM/ASA Journal on Uncertainty Quantification, 7 (4) , pp. 1323–1348, ISSN 2166-2525, doi: 10.1137/18M1216389
[bibtex]
[url] [pdf]
@ARTICLE{AR-PA-19-194,
author = {Mycek, P. and De Lozzo, M. },
title = {Multilevel Monte Carlo Covariance Estimation for the Computation of Sobol' Indices },
year = {2019},
number = {4},
volume = {7},
pages = {1323–1348},
issn = {2166-2525},
doi = {10.1137/18M1216389},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
keywords = {Monte Carlo, multilevel Monte Carlo, parameter estimation, uncertainty quantification, sensitivity analysis, Sobol' indices},
pdf = {https://doi.org/10.1137/18M1216389},
url = {https://epubs.siam.org/doi/pdf/10.1137/18M1216389}}
Contreras , A.A., Mycek, P., Le Maître, O.P., Rizzi, F., Debusschere, B. and Knio, O.M. (2018) Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations. Part A: Local Karhunen--Loève Representations, SIAM Journal on Scientific Computing, 40 (4) , pp. C520–C546, ISSN 1064-8275, doi: 10.1137/17M1132185
[bibtex] [pdf]
@ARTICLE{AR-PA-18-151,
author = {Contreras , A.A. and Mycek, P. and Le Maître, O.P. and Rizzi, F. and Debusschere, B. and Knio, O.M. },
title = {Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations. Part A: Local Karhunen--Loève Representations },
year = {2018},
number = {4},
volume = {40},
pages = {C520–C546},
issn = {1064-8275},
doi = {10.1137/17M1132185},
journal = {SIAM Journal on Scientific Computing},
pdf = {https://doi.org/10.1137/17M1132185},
supplementaryMaterial = {https://epubs.siam.org/doi/pdf/10.1137/17M1132197}}
Contreras , A.A., Mycek, P., Le Maître, O.P., Rizzi, F., Debusschere, B. and Knio, O.M. (2018) Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations Part B: Accelerated Monte Carlo Sampling with Local PC Expansions, SIAM Journal on Scientific Computing, 40 (4) , pp. C547–C580, ISSN 1064-8275, doi: 10.1137/17M1132197
[bibtex] [pdf]
@ARTICLE{AR-PA-18-152,
author = {Contreras , A.A. and Mycek, P. and Le Maître, O.P. and Rizzi, F. and Debusschere, B. and Knio, O.M. },
title = {Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations Part B: Accelerated Monte Carlo Sampling with Local PC Expansions },
year = {2018},
number = {4},
volume = {40},
pages = {C547–C580},
issn = {1064-8275},
doi = {10.1137/17M1132197},
journal = {SIAM Journal on Scientific Computing},
pdf = {https://doi.org/10.1137/17M1132197},
supplementaryMaterial = {https://epubs.siam.org/doi/pdf/10.1137/17M1132197}}
@CONFERENCE
Mycek, P. and De Lozzo, M. (2019) Multilevel Monte Carlo estimation of Sobol' indices for sensitivity analysis, Uncertainty Quantification & Optimization Conference (UQOP). UQOP 2019, Sorbonne University , Paris, France, 3 2019
[bibtex] [pdf]
@CONFERENCE{PR-PA-19-251,
author = {Mycek, P. and De Lozzo, M. },
title = {Multilevel Monte Carlo estimation of Sobol' indices for sensitivity analysis},
year = {2019},
month = {3},
booktitle = {Uncertainty Quantification & Optimization Conference (UQOP)},
organization = {UQOP 2019},
address = {Sorbonne University , Paris, France},
keywords = {Monte Carlo, Multilevel Monte Carlo, Covariance estimation, Sensitivity analysis, Sobol’ indices},
pdf = {https://uqop.sciencesconf.org/247415/document}}
Venkovic, N., Mycek, P., Giraud, L. and Le Maître, O.P. (2019) Recycling Krylov subspace strategies to solve stochastic elliptic equations, Uncertainty Quantification & Optimization Conference (UQOP). UQOP 2019, 3 2019
[bibtex] [pdf]
@CONFERENCE{PR-PA-19-252,
author = {Venkovic, N. and Mycek, P. and Giraud, L. and Le Maître, O.P. },
title = {Recycling Krylov subspace strategies to solve stochastic elliptic equations},
year = {2019},
month = {3},
booktitle = {Uncertainty Quantification & Optimization Conference (UQOP)},
organization = {UQOP 2019},
keywords = {Stochastic PDEs, Iterative solvers, Deflation, Monte Carlo, MCMC},
pdf = {https://uqop.sciencesconf.org/246800/document}}
De Lozzo, M., Mycek, P., Ricci, S., Rochoux, M., Roy, P., Goutal, N. and Ruede, U. (2017) Méthodes de Monte-Carlo multi-niveaux pour la quantification d’incertitudes et l’assimilation de données – Application à la modélisation fluviale, 49th Days of Statistics., Avignon, France, 6 2017
[bibtex]
@CONFERENCE{PR-CMGC-17-107,
author = {De Lozzo, M. and Mycek, P. and Ricci, S. and Rochoux, M. and Roy, P. and Goutal, N. and Ruede, U. },
title = {Méthodes de Monte-Carlo multi-niveaux pour la quantification d’incertitudes et l’assimilation de données – Application à la modélisation fluviale},
year = {2017},
month = {6},
booktitle = {49th Days of Statistics},
address = {Avignon, France}}
Mycek, P., De Lozzo, M., Ricci, S., Rochoux, M., Roy, P. and Goutal, N. (2017) Multilevel Monte Carlo estimation of covariances in the context of open-cahenne flow simulation CEMRACS 17/07-25/08/2017, CIRM, Marseille, 7 2017
[bibtex]
@CONFERENCE{PR-CMGC-17-300,
author = {Mycek, P. and De Lozzo, M. and Ricci, S. and Rochoux, M. and Roy, P. and Goutal, N. },
title = {Multilevel Monte Carlo estimation of covariances in the context of open-cahenne flow simulation},
year = {2017},
month = {7},
organization = {CEMRACS 17/07-25/08/2017, CIRM, Marseille}}
@TECHREPORT
Venkovic, N., Mycek, P., Giraud, L. and Le Maître, O.P. (2020) Comparative study of harmonic and Rayleigh-Ritz procedures with applications to deflated conjugate gradients, CERFACS, Technical report
[bibtex] [pdf]
@TECHREPORT{TR-PA-20-3,
author = {Venkovic, N. and Mycek, P. and Giraud, L. and Le Maître, O.P. },
title = {Comparative study of harmonic and Rayleigh-Ritz procedures with applications to deflated conjugate gradients},
year = {2020},
institution = {CERFACS},
address = {42 Avenue G. Coriolis, 31057 Toulouse Cedex 1, France},
type = {Technical report},
pdf = {https://hal.archives-ouvertes.fr/hal-02434043/}}
Mycek, P. and De Lozzo, M. (2018) Multilevel Monte Carlo covariance estimation for the computation of Sobol' indices, Cerfacs, Technical report
[bibtex] [pdf]
@TECHREPORT{TR-PA-18-128,
author = {Mycek, P. and De Lozzo, M. },
title = {Multilevel Monte Carlo covariance estimation for the computation of Sobol' indices},
year = {2018},
institution = {Cerfacs},
month = {9},
address = {42 avenue Gaspard Coriolis, 31057 Toulouse cedex 1},
type = {Technical report},
abstract = {Crude and quasi Monte Carlo (MC) sampling techniques are common tools dedicated to estimating statistics of a random quantity of interest, e.g. its expectation, variance or covariance.
We focus here on the uncertainty quantification framework where the quantity of interest is the output of a numerical simulator fed with uncertain (random) input parameters.
Then, sampling the output involves running the simulator for different samples of the inputs, which may be computationally time-consuming.
To reduce the cost of sampling, a first approach consists in replacing the numerical simulator by a surrogate model that is cheaper to evaluate, thus making it possible to generate more samples of the output and therefore leading to a lower sampling error.
However, this approach adds to the sampling error an unavoidable model error.
Another approach, which does not introduce any model error, is the so-called multilevel MC (MLMC) method.
Given a sequence of levels corresponding to numerical simulators with increasing accuracy and computational cost, MLMC combines samples obtained at different levels to construct an estimator at a reduced cost compared to standard MC sampling.
The number of levels and the sample sizes on each level may be determined by a sequential algorithm driven by a target accuracy.
In this paper, we extend theorems of MLMC theory dedicated to expectation and variance estimation to covariance estimation, and we propose a novel version of the multilevel algorithm, driven by a target cost.
These results are used in a sensitivity analysis context in order to derive a multilevel estimation of Sobol' indices, whose building blocks can be written as covariance terms in a pick-and-freeze formulation.
These theoretical and methodological contributions are successfully tested on an initial value problem with random parameters. },
keywords = {Monte Carlo, Multilevel Monte Carlo, Parameter estimation, Covariance, Uncertainty quantification, Sensitivity analysis, Sobol' indices},
pdf = {https://cerfacs.fr/wp-content/uploads/2018/09/TR-PA-18-128.pdf}}
