Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.
%0 Generic
%1 rehme2019bsplines
%A Rehme, Michael F.
%A Franzelin, Fabian
%A Pflüger, Dirk
%B Special issue on Surrogate Models for Uncertainty Quantification
%C Radarweg 29, 1043 NX Amsterdam, The Netherlands
%D 2019
%I Elsevier
%J Reliability Engineering and System Safety
%K B-splines Grid Simtech Sparse UQ Uncertaintysend:unibiblio myownsend:unibibliosend:unibibliosend:unibiblio
%T B-Splines on Sparse Grids for Surrogates in Uncertainty
Quantification
%X Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.
@preprint{rehme2019bsplines,
abstract = {Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.},
added-at = {2019-11-08T08:30:39.000+0100},
address = {Radarweg 29, 1043 NX Amsterdam, The Netherlands},
author = {Rehme, Michael F. and Franzelin, Fabian and Pflüger, Dirk},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2e713e387fceab5392f1023cdd980ef14/michaelrehme},
booktitle = {Special issue on Surrogate Models for Uncertainty Quantification},
interhash = {6595ddb3b0db0e1f58d85bd7f986fc55},
intrahash = {e713e387fceab5392f1023cdd980ef14},
journal = {Reliability Engineering and System Safety},
keywords = {B-splines Grid Simtech Sparse UQ Uncertaintysend:unibiblio myownsend:unibibliosend:unibibliosend:unibiblio},
publisher = {Elsevier},
timestamp = {2020-07-29T12:08:55.000+0200},
title = {B-Splines on Sparse Grids for Surrogates in Uncertainty
Quantification},
year = 2019
}
