Construction and Comparison of High-Dimensional Sobol' Generators

Sobol, I. M.; Asotsky, D. I.; Kreinin, Alexander; Kucherenko, Sergei

doi:10.1002/wilm.10056

Cited by 175 publications

(113 citation statements)

References 18 publications

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“…which comprises of 150,000 . The pseudo-random, uniformly distributed sampling is accomplished via mt19937ar Mersenne twister in MATLAB41, while the quasi-random sampling was accomplished via Sobol sequences42, which seek to maximally separate the sampled points in a deterministic manner in order to prevent clustering or gaps. We neglect the mean response term in the HDMR expansion, as there is no effective “mean” pillar.…”

Section: Resultsmentioning

confidence: 99%

Deep Learning for Flow Sculpting: Insights into Efficient Learning using Scientific Simulation Data

Stoecklein

Lore

Davies

et al. 2017

Sci Rep

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A new technique for shaping microfluid flow, known as flow sculpting, offers an unprecedented level of passive fluid flow control, with potential breakthrough applications in advancing manufacturing, biology, and chemistry research at the microscale. However, efficiently solving the inverse problem of designing a flow sculpting device for a desired fluid flow shape remains a challenge. Current approaches struggle with the many-to-one design space, requiring substantial user interaction and the necessity of building intuition, all of which are time and resource intensive. Deep learning has emerged as an efficient function approximation technique for high-dimensional spaces, and presents a fast solution to the inverse problem, yet the science of its implementation in similarly defined problems remains largely unexplored. We propose that deep learning methods can completely outpace current approaches for scientific inverse problems while delivering comparable designs. To this end, we show how intelligent sampling of the design space inputs can make deep learning methods more competitive in accuracy, while illustrating their generalization capability to out-of-sample predictions.

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Section: Resultsmentioning

confidence: 99%

Deep Learning for Flow Sculpting: Insights into Efficient Learning using Scientific Simulation Data

Stoecklein

Lore

Davies

et al. 2017

Sci Rep

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“…The computations were performed with both Sobol and modified Halton sequences. The implementations of these sequences are given in [12,17] and [13].…”

Section: Solving Integral Equations By Monte Carlo and Quasimonte Carmentioning

confidence: 99%

Energy Study of Monte Carlo and Quasi-Monte Carlo Algorithms for Solving Integral Equations

Gurov

Karaivanova

Alexandrov

2016

Procedia Computer Science

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In the past few years the development of exascale computing technology necessitated to obtain an estimate for the energy consumption when large-scale problems are solved with different high-performance computing (HPC) systems. In this paper we study the energy efficiency of a class of Monte Carlo (MC) and Quasi-Monte Carlo (QMC) algorithms for a given integral equation using hybrid HPC systems. The algorithms are applied to solve quantum kinetic integral equations describing ultra-fast transport in quantum wire. We compare the energy performance of the algorithms using a GPU-based computer platform and CPU-based computer platform both with and without hyper-threading (HT) technology. We use SPRNG library and CURAND generator to produce parallel pseudo-random (PPR) sequences for the MC algorithms on CPU-based and GPU -based platforms, respectively. For our QMC algorithms Sobol and Halton sequences are used to produce parallel quasi-random (PQR) sequences.We compare the obtained results of the tested algorithms with respect to the given energy metric. The results of our study demonstrate the importance of taking into account not only scalability of the HPC intensive algorithms but also their energy efficiency. They also show the need for further optimisation of the QMC algorithms when GPU-based computing platforms are used.

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“…Even if these techniques are designed for filling high-dimensional spaces (Sobol et al, 2011), they are not a viable solution when the computational cost of a single model simulation is high and the number of calls to the model becomes the bottleneck of the analysis. For this reason, some iterative sampling techniques aimed at adaptively guiding the system towards the critical condition have been proposed (Cadini et al, 2014; J. H. Li et al, 2011;Picheny et al, 2010;Turati et al, 2016a).…”

Section: Introductionmentioning

confidence: 99%

Simulation-based exploration of high-dimensional system models for identifying unexpected events

Turati

Pedroni

Zio

2017

Reliability Engineering & System Safety

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. Simulation-based exploration of highdimensional system models for identifying unexpected events. Reliability Engineering and System Safety.http://dx.doi.org/10.1016/j.ress.2017.04.004Simulation-based exploration of high-dimensional system models for identifying unexpected events AbstractMathematical numerical models are increasingly employed to simulate system behavior and identify sequences of events or configurations of the system's design and operational parameters that can lead the system to extreme conditions (Critical Region, CR). However, when a numerical model is: i) computationally expensive, ii) high-dimensional, and iii) complex, these tasks become challenging.In this paper, we propose an adaptive framework for efficiently tackling this problem: i) a dimensionality reduction technique is employed for identifying the factors and variables that most affect the system behavior; ii) a meta-model is sequentially trained to replace the computationally expensive model with a computationally cheap one; iii) an adaptive exploration algorithm based on Markov Chain Monte Carlo is introduced for exploring the system state space using the meta-model; iv) clustering and other techniques for the visualization of high dimensional data (e.g., parallel coordinates plot) are employed to summarize the retrieved information.The method is employed to explore a power network model involving 20 inputs. The CRs are properly identified with a limited computational cost, compared to another exploration technique of literature (i.e., Latin Hypercube Sampling).

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Construction and Comparison of High-Dimensional Sobol' Generators

Cited by 175 publications

References 18 publications

Deep Learning for Flow Sculpting: Insights into Efficient Learning using Scientific Simulation Data

Deep Learning for Flow Sculpting: Insights into Efficient Learning using Scientific Simulation Data

Energy Study of Monte Carlo and Quasi-Monte Carlo Algorithms for Solving Integral Equations

Simulation-based exploration of high-dimensional system models for identifying unexpected events

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