Mesh Optimization for Maxwell's Equations With Respect to Anisotropic Materials Using Geometric Algebra

Klimek, Mariusz; Schöps, Sebastian; Weiland, Thomas

doi:10.2528/pierm15110402

PIER M

2016

DOI: 10.2528/pierm15110402

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Mesh Optimization for Maxwell's Equations With Respect to Anisotropic Materials Using Geometric Algebra

Mariusz Klimek

Sebastian Schöps²,

Thomas Weiland³

Abstract: Clifford's Geometric Algebra provides an elegant formulation of Maxwell's equations in the space-time setting. Its clear geometric interpretation is used to derive a goal function, whose minimization results in Hodge-optimized material matrices being diagonal or diagonal-dominant. Effectively it is an optimization of the primal/dual mesh pair of a finite difference based discretization scheme taking into account the material properties. As a research example, a standing wave in 2D cavity filled with an anisotr… Show more

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“…The first true physics application was presented in Ref. [15]. The authors used Dense Neural Networks (DNN) in order to perform a variable transformation and demonstrate that they obtain significantly larger efficiencies for three body decay integrals than standard approaches [16].…”

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Event generation with normalizing flows

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We present a novel integrator based on normalizing flows which can be used to improve the unweighting efficiency of Monte-Carlo event generators for collider physics simulations. In contrast to machine learning approaches based on surrogate models, our method generates the correct result even if the underlying neural networks are not optimally trained. We exemplify the new strategy using the example of Drell-Yan type processes at the LHC, both at leading and partially at nextto-leading order QCD. I. INTRODUCTIONNumerical simulation programs are a cornerstone of collider physics. They are used for the planning of future experiments, analysis of current measurements and, finally, reinterpretation based on an improved theoretical understanding of nature. They employ Monte Carlo methods to link theory and experiment by generating virtual collider events, which can then be analyzed like actual events observed in detectors [1,2].With more and more data available from the Large Hadron Collider (LHC) and the high-luminosity upgrade, the task of simulating collisions at high precision becomes a matter of concern for the high-energy physics community. The projected amount of computational resources falls far short of the needs for precision event generation [3]. Past studies of the scaling behavior of multi-jet simulations have shown that the compute needs are largely determined by the gradually decreasing unweighting efficiency [4,5]. Except for dedicated integrators, which require a detailed understanding of the physics problem at hand, adaptive Monte-Carlo methods seem the only choice to address this problem [6][7][8][9][10][11][12][13].With the rise of machine learning, this topic has seen a resurgence of interest recently. The possibility of using these techniques for integration in high-energy physics was first discussed in Ref. [14]. Boosted Decision Trees and Generative Adversarial Networks (GANs) were investigated as possible general purpose integrators. This new technique improved the integration of non-separable high dimensional functions, for which traditional algorithms failed. The first true physics application was presented in Ref. [15]. The authors used Dense Neural Networks (DNN) in order to perform a variable transformation and demonstrate that they obtain significantly larger efficiencies for three body decay integrals than standard approaches [16]. The major drawback of this method is its computational cost. Since the network acts as a variable transformation, its gradient must be computed for each inference point in order to determine the Jacobian. This becomes computationally heavy for high multiplicity processes.A completely orthogonal approach utilizes machine learning techniques directly for amplitude evaluation [17] or event generation [18][19][20][21][22][23][24]. Training data for these approaches are obtained from traditional event generation techniques, and hence the problem of efficient event generation still remains. In addition, one needs to ensure that the neural networks are trained well ...

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Event generation with normalizing flows

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Mesh Optimization for Maxwell's Equations With Respect to Anisotropic Materials Using Geometric Algebra

Cited by 1 publication

References 11 publications

Event generation with normalizing flows

Event generation with normalizing flows

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