Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysis

Farcaș, Ionuț-Gabriel; Görler, T.; Bungartz, Hans‐Joachim; Jenko, F.; Neckel, Tobias

doi:10.1016/j.jcp.2020.109394

Cited by 13 publications

(40 citation statements)

References 29 publications

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“…To this end, we employ generalized, adaptive Smolyak approximations [39]. Smolyak's algorithm, also known as the combination scheme [17], is a strategy to construct multivariate sparse grid approximations by weakening the assumed coupling between the input dimensions (see, e.g., [6,11]). We briefly summarize Smolyak's algorithm.…”

Section: 3mentioning

confidence: 99%

“…For quadrature we employ a standard adaptive strategy. In the following, our notation is similar to [11].…”

Section: Dimension Adaptivity With Sparse Gridsmentioning

confidence: 99%

“…Adaptive refinement is preferred especially when the underlying problem has a richer structure, such as anisotropic coupling of the input parameters or lower intrinsic dimensionality -which is typically the case in most problems (see, e.g., [6,11,12,45]). The standard strategy is based on the dimension-adaptive algorithm of [15,19].…”

Section: Standard Dimension-adaptive Interpolation and Quadraturementioning

confidence: 99%

“…We address this by constructing adaptive sparse grid approximations based on weighted (L)-Leja sequences (see, e.g., [16,32]). Note that sparse grid approximations with Leja points have been devised for forward uncer-tainty propagation in [11,12,14,32]. In [11] the adaptive construction of the points is guided by sensitivity scores, and the strategy is applied in plasma microturbulence analysis.…”

mentioning

confidence: 99%

“…Note that sparse grid approximations with Leja points have been devised for forward uncer-tainty propagation in [11,12,14,32]. In [11] the adaptive construction of the points is guided by sensitivity scores, and the strategy is applied in plasma microturbulence analysis. In [14] the Leja points are constructed with the help of an adjoint-based error indicator.…”

mentioning

confidence: 99%

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Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems

Farcaș¹,

Latz²,

Ullmann³

et al. 2020

SIAM J. Sci. Comput.

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Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic quadrature is usually unable to efficiently investigate an informative and thus concentrated likelihood. This leads to a large number of required expensive evaluations of the mathematical model. To overcome these challenges, we formulate and test a multilevel adaptive sparse Leja algorithm. At each level, adaptive sparse grid interpolation and quadrature are used to approximate the posterior and perform all quadrature operations, respectively. Specifically, our algorithm uses coarse discretizations of the underlying mathematical model to investigate the parameter space and to identify areas of high posterior probability. Adaptive sparse grid algorithms are then used to place points in these areas, and ignore other areas of small posterior probability. The points are weighted Leja points. As the model discretization is coarse, the construction of the sparse grid is computationally efficient. On this sparse grid, the posterior measure can be approximated accurately with few expensive, fine model discretizations. The efficiency of the algorithm can be enhanced further by exploiting more than two discretization levels. We apply the proposed multilevel adaptive sparse Leja algorithm in numerical experiments involving elliptic inverse problems in 2D and 3D space, in which we compare it with Markov chain Monte Carlo sampling and a standard multilevel approximation.

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Section: 3mentioning

confidence: 99%

“…For quadrature we employ a standard adaptive strategy. In the following, our notation is similar to [11].…”

Section: Dimension Adaptivity With Sparse Gridsmentioning

confidence: 99%

Section: Standard Dimension-adaptive Interpolation and Quadraturementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems

Farcaș¹,

Latz²,

Ullmann³

et al. 2020

SIAM J. Sci. Comput.

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An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Galetzka

Loukrezis

Georg

et al. 2023

Numerical Meth Engineering

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This article introduces an hp-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either h-or p-refinement. The collocation method is based on weighted Leja nodes. After h-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner.For p-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.

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Prediction and reduction of runtime in non-intrusive forward UQ simulations

2019

Self Cite

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To foster predictive simulations, a variety of methods have recently been developed to efficiently tackle uncertainty quantification (UQ) in complex, computational intensive problems. Many of these methods are non-intrusive and, thus, result in a (large) number of embarrassingly parallel black-box evaluations of the underlying simulation codes. While the focus of development is typically on the number of black-box evaluations, which represents the bulk of the computational workload, an additional level of potential performance gains exists. In many scenarios, uncertain input leads not only to uncertain outputs, but also to a varying and thus stochastic runtime of the simulation codes. For scheduling the individual black-box runs, this information is typically not taken into account, resulting in non-negligible idling times on parallel systems. In this contribution, we compare a variety of different scheduling strategies for non-intrusive UQ scenarios using the non-intrusive polynomial chaos approach. In particular, we propose to construct a surrogate model for the runtime of the application using the identical UQ methodology as for the original problem. Using this model to predict the runtimes for subsequent black-box runs allows for (heuristical) optimization of the scheduling. The method has been tested for the forward quantification of uncertainty on academic models and on a pedestrian simulation in the context of evacuation scenarios. This approach allows speed-up factors of about two for the total runtime and can be generalised to a large variety of applications that incorporate parameter-dependent runtime.

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Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysis

Cited by 13 publications

References 29 publications

Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems

Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Prediction and reduction of runtime in non-intrusive forward UQ simulations

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