Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Farcaș, Ionuț-Gabriel; Peherstorfer, Benjamin; Neckel, Tobias; Jenko, F.; Bungartz, Hans‐Joachim

doi:10.1016/j.cma.2023.115908

Cited by 7 publications

(18 citation statements)

References 38 publications

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“…To address the practical limitations of full tensor grids, in [21,22], we proposed an efficient alternative approach called sensitivity-driven dimension-adaptive sparse grid interpolation. The new approach is based on adaptive sparse grids and Lagrange interpolation.…”

Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

“…For example, in a 5D parameter scan, using eight points in each direction leads to a full grid consisting of 8 5 = 32, 768 points in total. In contrast, a static sparse grid constructed as in [21,22] uses only 792 points.…”

Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

“…The cardinality of a static sparse grid can be further decreased by using adaptivity based on suitably chosen a posteriori refinement indicators. The strategy of [21,22] is to employ a greedy adaptive algorithm which exploits the fact that in most real-world problems (i) the underlying parameters are anisotropically coupled and (ii) only a subset of these parameters are important for the scan. To ascertain the importance and isotropy of the parameters in the scan, sensitivity information about the parameters is employed to ensure that the directions corresponding to parameters with the large sensitivity are preferentially refined.…”

Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

“…In this context, our main contribution in the present paper is to apply the newly developed sensitivity-driven dimensionadaptive sparse grid interpolation approach [21,22] to two important tasks. First, we use it to perform efficient parameter scans.…”

Section: Discharge Optimization Via High-dimensional Parameter Scansmentioning

confidence: 99%

“…This paper is organized as follows. In section 2, we summarize the sensitivity-driven dimension-adaptive sparse grid interpolation approach of [21,22]. In section 3, the sensitivity-driven approach is employed to perform a scan in a 21 parameter setting, at one perpendicular wave-number.…”

Section: Outline Of This Papermentioning

confidence: 99%

See 4 more Smart Citations

Turbulence suppression by energetic particles: a sensitivity-driven dimension-adaptive sparse grid framework for discharge optimization

Farcaș¹,

Siena

Jenko

2021

Nucl. Fusion

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A newly developed sensitivity-driven approach is employed to study the role of energetic particles in suppressing turbulence-inducing micro-instabilities for a set of realistic JET-like cases with NBI deuterium and ICRH 3He fast ions. First, the efficiency of the sensitivity-driven approach is showcased for scans in a 21-dimensional parameter space, for which only 250 simulations are necessary. The same scan performed with traditional Cartesian grids with only two points in each of the 21 dimensions would require 221 = 2, 097, 152 simulations. Then, a 14-dimensional parameter subspace is considered, using the sensitivity-driven approach to find an approximation of the parameter-to-growth rate map averaged over nine bi-normal wave-numbers, indicating pathways towards turbulence suppression. The respective turbulent fluxes, obtained via nonlinear simulations for the optimized set of parameters, are reduced by more than two order of magnitude compared to the reference results.

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Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

Section: Sensitivity-driven Dimension-adaptive Sparse Grid Interpolationmentioning

confidence: 99%

Section: Discharge Optimization Via High-dimensional Parameter Scansmentioning

confidence: 99%

Section: Outline Of This Papermentioning

confidence: 99%

See 3 more Smart Citations

Turbulence suppression by energetic particles: a sensitivity-driven dimension-adaptive sparse grid framework for discharge optimization

Farcaș¹,

Siena

Jenko

2021

Nucl. Fusion

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Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

Gao,

Iyama,

Itoi

2024

Japan Architectural Review

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This study introduces an approach for probabilistic seismic performance estimation, which focuses on the probability of intensity measures exceeding a specified value based on engineering demand parameters. Conventional methods face challenges owing to the increase in computational costs associated with the uncertainties in earthquake scenarios. To address this, we use high‐fidelity (HF) and low‐fidelity (LF) model data to develop a multilevel hierarchy of surrogate models, which improves the simulation‐based probabilistic estimation. However, designing a reliable LF model and ensuring the accuracy of the surrogate model hierarchy remains challenging. Herein, we present a multi‐fidelity Monte Carlo (MFMC) predictor combined with a conventional surrogate model to improve probabilistic seismic performance estimation, thereby leveraging LF model efficiency and HF data accuracy for unbiased results. We addressed the challenge of constructing a suitable LF model by using a surrogate model trained from limited HF data. The MFMC predictor improves the accuracy of probabilistic analysis than the surrogate models trained from limited HF data. Further, the automatic relevance determination method is introduced to select the most appropriate inputs for the surrogate model. A case study featuring a special moment‐resistant frame, subject to uncertainties from both ground motion and structural properties, illustrates the efficiency of the method. A LF model is developed using the Kriging method, followed by the construction of the MFMC predictor for probabilistic analysis, thereby leveraging both limited HF and numerous LF data. Comparing the exceedance probability curves obtained from the MFMC predictor with those from direct Monte Carlo simulations and conventional Kriging showed that our proposed method offers a promising tool for probabilistic seismic performance estimation under uncertainty.

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Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization

Law,

Cerfon,

Peherstorfer

et al. 2023

Journal of Computational Physics

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Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Cited by 7 publications

References 38 publications

Turbulence suppression by energetic particles: a sensitivity-driven dimension-adaptive sparse grid framework for discharge optimization

Turbulence suppression by energetic particles: a sensitivity-driven dimension-adaptive sparse grid framework for discharge optimization

Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization

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