Monte Carlo analysis of reactivity coefficients in fast reactors general theory and applications

Miller, L. B.

doi:10.2172/4500721

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…Due to the many origins and applications, the method is known under several names, the most popular being delta tracking, Woodcock tracking, pseudo scattering, and the null‐collision algorithm. Despite being very intuitive, it took several years until the correctness of the algorithms was proved rigorously [Mil67, Col68]. Recently, Galtier et al [GBC*13] presented a derivation of the algorithm directly from the RTE, demonstrating not only the correctness, but also providing a convenient framework for postulating new variants of the algorithm.…”

Section: Distance Samplingmentioning

confidence: 99%

“…The distribution of distances to the first real collision in the combined medium corresponds to free‐path distribution in the original medium, i.e. the PDF of free‐path samples produced by delta tracking is μ t ( y ) T ( x , y ) [Col68, Mil67]. However, the main drawback of delta tracking is that, because of the exponentiated heterogeneous integral in T ( x , y ), we cannot compute the actual value of the PDF.…”

Section: Distance Samplingmentioning

confidence: 99%

“…The above formalization of weighted delta tracking was inspired by the integral formulation of null‐collision algorithms developed in particle‐transport physics by Galtier et al [GBC*13] and recently adopted in computer graphics by Kutz et al [KHLN17]. Since the integral formulation is derived from the RTE, it directly demonstrates the correctness of null collision algorithms without relying on constraining physical interpretations or involved mathematical proofs [Col68,Mil67]. To that end, Galtier et al first apply a number of identities to the RTE to obtain a formulation that can be trivially turned into a Monte Carlo estimator.…”

Section: Distance Samplingmentioning

confidence: 99%

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Monte Carlo Methods for Volumetric Light Transport Simulation

Novák

Georgiev

Hanika

et al. 2018

Computer Graphics Forum

104

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The wide adoption of path‐tracing algorithms in high‐end realistic rendering has stimulated many diverse research initiatives. In this paper we present a coherent survey of methods that utilize Monte Carlo integration for estimating light transport in scenes containing participating media. Our work complements the volume‐rendering state‐of‐the‐art report by Cerezo et al. [CPP*05]; we review publications accumulated since its publication over a decade ago, and include earlier methods that are key for building light transport paths in a stochastic manner. We begin by describing analog and non‐analog procedures for free‐path sampling and discuss various expected‐value, collision, and track‐length estimators for computing transmittance. We then review the various rendering algorithms that employ these as building blocks for path sampling. Special attention is devoted to null‐collision methods that utilize fictitious matter to handle spatially varying densities; we import two “next‐flight” estimators originally developed in nuclear sciences. Whenever possible, we draw connections between image‐synthesis techniques and methods from particle physics and neutron transport to provide the reader with a broader context.

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Section: Distance Samplingmentioning

confidence: 99%

Section: Distance Samplingmentioning

confidence: 99%

Section: Distance Samplingmentioning

confidence: 99%

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Monte Carlo Methods for Volumetric Light Transport Simulation

Novák

Georgiev

Hanika

et al. 2018

Computer Graphics Forum

104

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“…Development of the estimator. The score function estimator is one of the first types of estimators to be derived, initially by several different groups in the 1960s, including Miller (1967) in the design of stable nuclear reactors, and by Rubinstein (1969) in the early development of Monte Carlo optimisation. Later the estimator was derived and applied by Rubinstein and Kreimer (1983) for discrete-event systems in operations research, where they began to refer to the estimator as the score function method, the name we use in this paper.…”

Section: Research In Score Function Gradient Estimationmentioning

confidence: 99%

Monte Carlo Gradient Estimation in Machine Learning

Mohamed¹,

Roșca²,

Figurnov³

et al. 2019

Preprint

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This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies-the pathwise, score function, and measure-valued gradient estimatorsexploring their historical developments, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

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“…To the best of our knowledge the SF method in a simulation context was introduced independently in the late 1960s by Aleksandrov, Sysoyev and Shemeneva (1968), Mikhailov (1967), Miller (1967, and Rubinstein (1969). Related references in the early 1980s are Ermakov and Mikhailov (1982), Kreimer (1984), and Rubinstein and Kreimer (1983).…”

Section: Introductionmentioning

confidence: 99%

Optimization and sensitivity analysis of computer simulation models by the score function method

Kleijnen

Rubinstein

1996

European Journal of Operational Research

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Monte Carlo analysis of reactivity coefficients in fast reactors general theory and applications

Cited by 8 publications

References 18 publications

Monte Carlo Methods for Volumetric Light Transport Simulation

Monte Carlo Methods for Volumetric Light Transport Simulation

Monte Carlo Gradient Estimation in Machine Learning

Optimization and sensitivity analysis of computer simulation models by the score function method

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