Quasi-Monte Carlo Software

Choi, Sou‐Cheng T.; Hickernell, Fred J.; Jagadeeswaran, R.; McCourt, Michael; G., Sorokin, Aleksei

doi:10.1007/978-3-030-98319-2_2

Cited by 8 publications

(3 citation statements)

References 30 publications

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“…One well‐established quasi‐random sequence is the Sobol sequence, developed for use in Monte Carlo integration 12,16,17 . Figure 5A shows the first 32 points in the two‐dimensional Sobol sequence as implemented in the Python library SciPy 11,16,18 .…”

Section: Methodsmentioning

confidence: 99%

“…14,15 One well-established quasi-random sequence is the Sobol sequence, developed for use in Monte Carlo integration. 12,16,17 Figure 5A shows the first 32 points in the two-dimensional Sobol sequence as implemented in the Python library SciPy. 11,16,18 The points are more uniformly distributed than those of a random sequence 14 but there is still noticeable discrepancy in sampling.…”

Section: Random and Quasi-random Sampling Sequencesmentioning

confidence: 99%

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High‐throughput determination of grain size distributions by EBSD with low‐discrepancy sampling

Long,

Holbrook,

Hufnagel

et al. 2023

Journal of Microscopy

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Because microstructure plays an important role in the mechanical properties of structural materials, developing the capability to quantify microstructures rapidly is important to enabling high‐throughput screening of structural materials. Electron backscatter diffraction (EBSD) is a common method for studying microstructures and extracting information such as grain size distributions (GSDs), but is not particularly fast and thus could be a bottleneck in high‐throughput systems. One approach to accelerating EBSD is to reduce the number of points that must be scanned. In this work, we describe an iterative method for reducing the number of scan points needed to measure GSDs using incremental low‐discrepancy sampling, including on‐the‐fly grain size calculations and a convergence test for the resulting GSD based on the Kolmogorov–Smirnov test. We demonstrate this method on five real EBSD maps collected from magnesium AZ31B specimens and compare the effectiveness of sampling according to two different low discrepancy sequences, the Sobol and R2 sequences, and random sampling. We find that R2 sampling is able to produce GSDs that are statistically very similar to the GSDs of the full density grids using, on average, only 52% of the total scan points. For EBSD maps that contained monodisperse GSDs and over 1000 grains, R2 sampling only required an average of 39% of the total EBSD points.

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Section: Methodsmentioning

confidence: 99%

Section: Random and Quasi-random Sampling Sequencesmentioning

confidence: 99%

High‐throughput determination of grain size distributions by EBSD with low‐discrepancy sampling

Long,

Holbrook,

Hufnagel

et al. 2023

Journal of Microscopy

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“…At its core, UM-Bridge consists of an HTTPbased protocol mirroring the mathematical interface above. Integrations for (currently) C++, R, Python, MUQ (Parno et al, 2021), QMCPy (Choi et al, 2020+) and PyMC (Salvatier et al, 2016) are provided for convenience. This approach has a number of benefits:…”

Section: Statement Of Needmentioning

confidence: 99%

UM-Bridge: Uncertainty quantification and modeling bridge

Seelinger¹,

Cheng-Seelinger²,

Davis³

et al. 2023

JOSS

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UM-Bridge (the uncertainty quantification (UQ) and modeling bridge) provides a unified interface for numerical models that is accessible from any programming language or framework. It is primarily intended for coupling advanced models (e.g., simulations of complex physical processes) to advanced statistical or optimization methods for UQ without requiring the model and UQ algorithms to share a common computational environment.

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On Dropping the First Sobol’ Point

Owen

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Quasi-Monte Carlo Software

Cited by 8 publications

References 30 publications

High‐throughput determination of grain size distributions by EBSD with low‐discrepancy sampling

High‐throughput determination of grain size distributions by EBSD with low‐discrepancy sampling

UM-Bridge: Uncertainty quantification and modeling bridge

On Dropping the First Sobol’ Point

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