Computational efficiencies of approximated exponential functions for transport calculations of the characteristics method

Yamamoto, Akio; Kitamura, Yasunori; Yamane, Yoshihiro

doi:10.1016/j.anucene.2004.01.003

Cited by 21 publications

(11 citation statements)

References 2 publications

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“…Visually, we can see that the output of NN with the LUT approximation technique is very close to the output of NN with no approximation. As stated in [15], using LUT approximation technique improves runtime performance with an acceptable accuracy for NN as shown in Figures 5 and 6. In general, this improvement in runtime leads to more energy efficiency (calculated using equation (9)).…”

Section: Using Alternative Lower Energy Kernelsmentioning

confidence: 66%

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A design methodology for energy aware neural networks

Dabbagh

Hajj

Chehab

et al. 2011

2011 7th International Wireless Communications and Mobile Computing Conference

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The increasing demand for mobile devices and high performance computing has made energy consumption a main issue in computer technology. Mobile devices require extended battery life, but the available technology still puts limits on the need for recharging the devices. High performance computing has a high price tag on energy for compute-intensive applications such as data mining. As a result, optimizations at various layers of the computer platform are becoming necessary to minimize energy usage or extend the time before a battery needs to be recharged. This paper focuses on back-propagation neural network algorithm, one of the popular compute-intensive data mining algorithms. The goal is to present a design methodology for developing an energy aware algorithm. The key idea revolves around identifying operations called kernels, which are frequently used in the algorithm, and that can be implemented in hardware. Optimizing these kernels for performance or energy would then lead to a major impact in these areas. These kernels are analyzed for their impact on the overall application energy using energy-based asymptotic analysis. The methodology then considers additional optimizations not related to kernels, but are specific to the back-propagation algorithm. Suggestions are provided to improve the performance and reduce energy consumption. Experiments show that there are significant potentials in energy reduction through the use of alternative lower energy kernels or through custom optimizations with tradeoffs in the accuracy of the results.

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Section: Using Alternative Lower Energy Kernelsmentioning

confidence: 66%

“…We examine the use of approximation techniques [15] instead of exact calculation of the exponential function.…”

Section: Using Alternative Lower Energy Kernelsmentioning

confidence: 99%

A design methodology for energy aware neural networks

Dabbagh

Hajj

Chehab

et al. 2011

2011 7th International Wireless Communications and Mobile Computing Conference

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“…25 Using this formalism for MSλD, it is the values of θ that have fictious masses, m θ , and are propagated through the equations of motion, not the λ values directly. Thus, the extended Hamiltonian is:

H_{o} true(X, false{x false}, false{λ false(θ true) false} true) = T_{x} + T_{θ} + V true(X, false{x false}, true{λ false(θ false) false} true)

…”

Section: Methodsmentioning

confidence: 99%

“…The functional forms of {k} that are assessed in this work are listed in Table 1 along with their corresponding partial derivatives with respect to y. Lookup tables were used to efficiently approximate k Nexp . [25] Using this formalism for MSkD, it is the values of y that have fictious masses, m y , and are propagated through the equations of motion, not the k values directly. Thus, the extended Hamiltonian is:…”

Section: Multisite K-dynamics Theorymentioning

confidence: 99%

Applying efficient implicit nongeometric constraints in alchemical free energy simulations

2011

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Several strategies have been developed for satisfying bond lengths, angle and other geometric constraints in molecular dynamics simulations. Advanced variations of alchemical free energy perturbation simulations, however, also require non-geometric constraints. In our recently developed Multi-Site λ-dynamics simulation method, the conventional λ parameters that are associated with the progress variables in alchemical transformations are treated as dynamic variables and are constrained such that: 0 ≤ λi ≤ 1 and ∑i=1Nλi=1 . Here, we present four functional forms of λ that implicitly satisfy these non-geometric constraints, whose values and forces are facile to compute and that yield stable simulations using a 2 fs integration timestep. Using model systems, we present the sampling characteristics of these functional forms and demonstrate the enhanced sampling profiles and improved convergence rates that are achieved by the functional form: λi=ecsinθi∑j=1Necsinθj that oscillates between λi=0 and λi=1 and has relatively steep transitions between these endpoints.

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“…It is interesting to note at this stage that the Step Characteristics scheme presents a higher arithmetic intensity than the Diamond Differencing: although both schemes require the same information being fetched from memory 5 (l, Σ, Q), the DD scheme requires only a few operations to process them, whereas the SC scheme requires computing an expensive exponential (even though tabulating the exponential function somewhat reduces its computational cost, (11) the SC scheme still remains more arithmetically intensive than the DD scheme).…”

Section: Integration Schemesmentioning

confidence: 99%

Vectorization of a 2D–1D Iterative Algorithm for the 3D Neutron Transport Problem in Prismatic Geometries

Moustafa¹,

Févotte²,

Lathuilière³

et al. 2014

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo

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The past few years have been marked by a noticeable increase in the interest in 3D whole-core heterogeneous deterministic neutron transport solvers for reference calculations. Due to the extremely large problem sizes tackled by such solvers, they need to use adapted numerical methods and need to be efficiently implemented to take advantage of the full computing power of modern systems. As for numerical methods, one possible approach consists in iterating over resolutions of 2D and 1D MOC problems by taking advantage of prismatic geometries. The MICADO solver, developed at EDF R&D, is a parallel implementation of such a method in distributed and shared memory systems. However it is currently unable to use SIMD vectorization to leverage the full computing power of modern CPUs. In this paper, we describe our first effort to support vectorization in MICADO, typically targeting Intel c SSE CPUs. Both the 2D and 1D algorithms are vectorized, allowing for high expected speedups for the whole spatial solver. We present benchmark computations, which show nearly optimal speedups for our vectorized implementation on the TAKEDA case.

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Computational efficiencies of approximated exponential functions for transport calculations of the characteristics method

Cited by 21 publications

References 2 publications

A design methodology for energy aware neural networks

A design methodology for energy aware neural networks

Applying efficient implicit nongeometric constraints in alchemical free energy simulations

Vectorization of a 2D–1D Iterative Algorithm for the 3D Neutron Transport Problem in Prismatic Geometries

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