Hierarchical Latin Hypercube Sampling

Garg, Vikram; Stogner, Roy H.

doi:10.1080/01621459.2016.1158717

Cited by 12 publications

(6 citation statements)

References 8 publications

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“…We sample the points in the parameter space defined in Table 2 using LHS, as we have done already in Euclid Collaboration: Knabenhans et al (2019). LHS is a very straightforward sampling technique that is widely used and accepted in the cosmological emulator community (Heitmann et al 2009(Heitmann et al , 2010(Heitmann et al , 2014Nishimichi et al 2019;DeRose et al 2019;Gration & Wilkinson 2019;Rogers et al 2019) and extensively presented in the statistical sampling literature (McKay et al 1979;Tang 1993;Liefvendahl & Stocki 2006;Crombecq et al 2011;Damblin et al 2013;Sheikholeslami & Razavi 2017;Yang et al 2017;Garg & Stogner 2017;Swiler et al 2006). Endowed with an additional optimisation step (we use a distance-based criterion), its main advantage is that it combines good space-filling properties with a high degree of randomness.…”

Section: Experimental Design: Samplingmentioning

confidence: 99%

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

Knabenhans

Stadel

Potter

et al. 2021

Monthly Notices of the Royal Astronomical Society

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We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent-level accurate emulation is now supported in the eight-dimensional parameter space of w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h−1 Gpc)3 volumes based on paired-and-fixed initial conditions and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter wa significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors like HALOFIT, HMCode and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of $1{{\ \rm per\ cent}}$ or better for 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1 and z ≤ 3 compared to high-resolution dark matter only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.

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Section: Experimental Design: Samplingmentioning

confidence: 99%

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

Knabenhans

Stadel

Potter

et al. 2021

Monthly Notices of the Royal Astronomical Society

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“…Monte Carlo sampling and LHS are the sampling tools used in this work, and a description of each follows. MCS is a commonly used technique of random sampling probability distributions, and the generated sampled values can be randomly from anywhere within variability space.…”

Section: Metamodeling Methodsmentioning

confidence: 99%

“…MCS is used in this work for the testing data set. LHS aims at randomly sampling the given probability distributions of the variability parameters more effectively than MCS. This goal is achieved by stratifying the probability distributions into equal intervals on the cumulative scale [0, 1] and then complete random sampling within each interval, which avoids clustering the generated numbers.…”

Section: Metamodeling Methodsmentioning

confidence: 99%

Efficient yield estimation of multiband patch antennas by polynomial chaos‐based Kriging

Leifsson

Koziel

2020

Int J Numerical Modelling

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Yield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since direct Monte Carlo sampling of accurate physics-based models can be computationally intensive, this work proposes the use of the polynomial chaos-Kriging (PC-Kriging) metamodeling method for fast yield estimation of multiband patch antennas. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel since the PCE is good at capturing the function tendency and Kriging is good at matching the observations at training points. The PC-Kriging method is demonstrated on two analytical cases and two multiband patch antenna cases and is compared with the PCE and Kriging metamodeling methods. In the analytical cases, PC-Kriging reduces the computational cost by over 40% compared with PCE and over 94% compared with Kriging. In the antenna cases, PC-Kriging reduces the computational cost by over 60% compared with Kriging and over 90% compared with PCE. In all cases, the savings are obtained without compromising the accuracy. K E Y W O R D S antenna yield estimation, Kriging, microstrip multiband patch antenna, Monte Carlo sampling, polynomial chaos expansions, polynomial chaos-based Kriging

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“…Sufficient sampling iterations tend to generate the convergence to the pre-defined probability distributions. MCS (Metropolis and Ulam, 1949) and LHS (Garg and Stogner, 2017) are the sampling tools used in this work and a description of each follows. MCS (Metropolis and Ulam, 1949) is a commonly used technique of random sampling probability distributions and the generated sampled values can be randomly from anywhere within variability space.…”

Section: Samplingmentioning

confidence: 99%

“…LHS (Garg and Stogner, 2017) aims at random sampling the given probability distributions of the variability parameters more effectively than MCS. This goal is achieved by stratifying the probability distributions into equal intervals on the cumulative scale [0, 1].…”

Section: Samplingmentioning

confidence: 99%

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

Leifsson

2019

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Purpose Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models. Design/methodology/approach In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels. Findings To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent. Originality/value The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

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Hierarchical Latin Hypercube Sampling

Cited by 12 publications

References 8 publications

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

Efficient yield estimation of multiband patch antennas by polynomial chaos‐based Kriging

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

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