7 research outputs found
Kontextsensitive Modellhierarchien für Quantifizierung der höherdimensionalen Unsicherheit
We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-Mikroinstabilitätssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als Standardansätze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewältigen können
A general framework for quantifying uncertainty at scale
In many fields of science, comprehensive and realistic computational models
are available nowadays. Often, the respective numerical calculations call for
the use of powerful supercomputers, and therefore only a limited number of
cases can be investigated explicitly. This prevents straightforward approaches
to important tasks like uncertainty quantification and sensitivity analysis.
This challenge can be overcome via our recently developed sensitivity-driven
dimension adaptive sparse grid interpolation strategy. The method exploits, via
adaptivity, the structure of the underlying model (such as lower intrinsic
dimensionality and anisotropic coupling of the uncertain inputs) to enable
efficient and accurate uncertainty quantification and sensitivity analysis at
scale. We demonstrate the efficiency of our approach in the context of fusion
research, in a realistic, computationally expensive scenario of turbulent
transport in a magnetic confinement tokamak device with eight uncertain
parameters, reducing the effort by at least two orders of magnitude. In
addition, we show that our method intrinsically provides an accurate surrogate
model that is nine orders of magnitude cheaper than the high-fidelity model.Comment: 19 pages, 6 figures, 1 tabl
Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models
for variance reduction to make tractable uncertainty quantification even when
numerically simulating the physical systems of interest with high-fidelity
models is computationally expensive. This work proposes a context-aware
multi-fidelity Monte Carlo method that optimally balances the costs of training
low-fidelity models with the costs of Monte Carlo sampling. It generalizes the
previously developed context-aware bi-fidelity Monte Carlo method to
hierarchies of multiple models and to more general types of low-fidelity
models. When training low-fidelity models, the proposed approach takes into
account the context in which the learned low-fidelity models will be used,
namely for variance reduction in Monte Carlo estimation, which allows it to
find optimal trade-offs between training and sampling to minimize upper bounds
of the mean-squared errors of the estimators for given computational budgets.
This is in stark contrast to traditional surrogate modeling and model reduction
techniques that construct low-fidelity models with the primary goal of
approximating well the high-fidelity model outputs and typically ignore the
context in which the learned models will be used in upstream tasks. The
proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies
of a wide range of types of low-fidelity models such as sparse-grid and
deep-network models. Numerical experiments with the gyrokinetic simulation code
\textsc{Gene} show speedups of up to two orders of magnitude compared to
standard estimators when quantifying uncertainties in small-scale fluctuations
in confined plasma in fusion reactors. This corresponds to a runtime reduction
from 72 days to about four hours on one node of the Lonestar6 supercomputer at
the Texas Advanced Computing Center.Comment: 25 pages, 12 figures, 3 table
Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis
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 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.Comment: 28 pages, 9 figures, 11 table