TY - GEN
T1 - A least-squares, adaptive uncertainty propagation approach for a plasma-coupled combustion system
AU - Tang, Kunkun
AU - Massa, Luca
AU - Wang, Jonathan
AU - Freund, Jonathan B.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016
Y1 - 2016
N2 - We employ a new stochastic methodology for the construction of surrogate models for uncertainty quantification (UQ) and sensitivity analysis (SA). It is based on polynomial dimensional decomposition (PDD), as are widely used in solving high-dimensional stochastic problems that arise in various applications. In our approach, the coefficients of the PDD expansion are determined by using a least-squares regression (LSR). Compared to a projection approach, the use of LSR not only avoids the computation of high-dimensional integrals, but also affords an attractive flexibility in choosing the sampling points, which facilitates importance sampling using a calibrated posterior distribution based on a Bayesian approach. LSR can be particularly advantageous in cases where the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense, focusing effort on efficient finite-resolution sampling. To efficiently include parameter spaces with a moderate number of uncertain parameters (up to 7 in this work), the PDD is coupled with an adaptive ANOVA (analysis of variance) decomposition. This provides an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational overhead cost of a high-dimensional expansion. In addition, the PDD representation of the ANOVA component functions is further simplified in an adaptive way according to the relative contribution of the different polynomials to the variance. The overall methodology is demonstrated on plasma-mediated ignition simulations as part of a large predictive science effort in the Center for Exascale Simulation of Plasma-Coupled Combustion (XPACC). The specific configuration we study includes model parameters arising from reaction rates in a global chemical kinetics description, and a laser-induced breakdown ignition seed.
AB - We employ a new stochastic methodology for the construction of surrogate models for uncertainty quantification (UQ) and sensitivity analysis (SA). It is based on polynomial dimensional decomposition (PDD), as are widely used in solving high-dimensional stochastic problems that arise in various applications. In our approach, the coefficients of the PDD expansion are determined by using a least-squares regression (LSR). Compared to a projection approach, the use of LSR not only avoids the computation of high-dimensional integrals, but also affords an attractive flexibility in choosing the sampling points, which facilitates importance sampling using a calibrated posterior distribution based on a Bayesian approach. LSR can be particularly advantageous in cases where the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense, focusing effort on efficient finite-resolution sampling. To efficiently include parameter spaces with a moderate number of uncertain parameters (up to 7 in this work), the PDD is coupled with an adaptive ANOVA (analysis of variance) decomposition. This provides an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational overhead cost of a high-dimensional expansion. In addition, the PDD representation of the ANOVA component functions is further simplified in an adaptive way according to the relative contribution of the different polynomials to the variance. The overall methodology is demonstrated on plasma-mediated ignition simulations as part of a large predictive science effort in the Center for Exascale Simulation of Plasma-Coupled Combustion (XPACC). The specific configuration we study includes model parameters arising from reaction rates in a global chemical kinetics description, and a laser-induced breakdown ignition seed.
KW - Adaptive ANOVA
KW - Combustion
KW - Polynomial dimensional decomposition (PDD)
KW - Sensitivity analysis
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=84995494407&partnerID=8YFLogxK
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U2 - 10.7712/100016.2253.9160
DO - 10.7712/100016.2253.9160
M3 - Conference contribution
AN - SCOPUS:84995494407
T3 - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
SP - 6213
EP - 6225
BT - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
A2 - Papadopoulos, V.
A2 - Stefanou, G.
A2 - Plevris, V.
A2 - Papadrakakis, M.
PB - National Technical University of Athens
T2 - 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016
Y2 - 5 June 2016 through 10 June 2016
ER -