TY - JOUR
T1 - Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis
AU - Konrad, Julia
AU - Farcaş, Ionuţ Gabriel
AU - Peherstorfer, Benjamin
AU - Di Siena, Alessandro
AU - Jenko, Frank
AU - Neckel, Tobias
AU - Bungartz, Hans Joachim
N1 - Funding Information:
I.-G.F., A.D.S. and F.J. were supported by the Exascale Computing Project (No. 17-SC-20-SC ), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. B.P. acknowledges support by the National Science Foundation under grants CMMI-1761068 and IIS-1901091 . We gratefully acknowledge the compute and data resources provided by the Leibniz Supercomputing Centre ( www.lrz.de ).
Funding Information:
I.-G.F. A.D.S. and F.J. were supported by the Exascale Computing Project (No. 17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. B.P. acknowledges support by the National Science Foundation under grants CMMI-1761068 and IIS-1901091. We gratefully acknowledge the compute and data resources provided by the Leibniz Supercomputing Centre (www.lrz.de).
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022/2/15
Y1 - 2022/2/15
N2 - The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the background plasma and the magnetic equilibrium. Therefore, uncertainty quantification is essential for achieving predictive numerical simulations of plasma turbulence. However, the high computational costs of the required gyrokinetic simulations and the large number of parameters render standard Monte Carlo techniques intractable. To address this problem, we propose a multi-fidelity Monte Carlo approach in which we employ data-driven low-fidelity models that exploit the structure of the underlying problem such as low intrinsic dimension and anisotropic coupling of the stochastic inputs. The low-fidelity models are efficiently constructed via sensitivity-driven dimension-adaptive sparse grid interpolation using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the power of this method by applying it to two plasma turbulence problems with up to 14 stochastic parameters, demonstrating that it is up to four orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance, which translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.
AB - The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the background plasma and the magnetic equilibrium. Therefore, uncertainty quantification is essential for achieving predictive numerical simulations of plasma turbulence. However, the high computational costs of the required gyrokinetic simulations and the large number of parameters render standard Monte Carlo techniques intractable. To address this problem, we propose a multi-fidelity Monte Carlo approach in which we employ data-driven low-fidelity models that exploit the structure of the underlying problem such as low intrinsic dimension and anisotropic coupling of the stochastic inputs. The low-fidelity models are efficiently constructed via sensitivity-driven dimension-adaptive sparse grid interpolation using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the power of this method by applying it to two plasma turbulence problems with up to 14 stochastic parameters, demonstrating that it is up to four orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance, which translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.
KW - Multi-fidelity Monte Carlo sampling
KW - Plasma micro-turbulence
KW - Reduced-dimension low-fidelity models
KW - Sensitivity-driven adaptivity
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U2 - 10.1016/j.jcp.2021.110898
DO - 10.1016/j.jcp.2021.110898
M3 - Article
AN - SCOPUS:85121356240
SN - 0021-9991
VL - 451
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 110898
ER -