Variance Reduction
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2022 ◽  
Vol 32 (1) ◽  
pp. 1-28
Ran Xin ◽  
Usman A. Khan ◽  
Soummya Kar

2021 ◽  
Peng Lu ◽  
Qiuran Wu ◽  
Hua Du ◽  
Yu Zheng ◽  
Xiaokang Zhang ◽  

Abstract The neutron induced irradiation field is a key problem in fusion reactor related to nuclear responses, shielding design, nuclear safety, and thermo-hydraulic analysis. To support the system design of China Fusion Engineering Test Reactor (CFETR), the comprehensive analysis of irradiation field has been conducted in support of many new developed advanced tools. The paper first summarizes the recent progress on related neutronics code development effort including the geometry conversion tool cosVMPT, Monte Carlo variance reduction technology ‘on-the-fly’ global variance reduction (GVR). Such developed tools have been fully validated and applied on the CFETR nuclear analysis. The neutron irradiation has been evaluated on CFETR Water Cooled Ceramic Breeder (WCCB) blanket, divertor, vacuum vessel, superconductive coils and four kinds of heating systems including the Electron Cyclotron Resonance Heating (ECRH), Ion Cyclotron Resonance Heating (ICRH), Low Hybrid Wave (LHW) and Neutral Beam Injection (NBI). The nuclear responses of tritium breeding ratio (TBR), heating, irradiation damage, Hydrogen/Helium (H/He) production rate of material have been analyzed. In case of neutron damage and overheating deposition on the superconductive coils and Vacuum Vessel (VV), the interface and shielding design among heating systems, blanket and other systems has been initialized. The results show the shielding design can meet the requirement of coil and VV after several iterated neutronics calculation.

2021 ◽  
Vol 10 (4) ◽  
pp. 192

Value at Risk (VaR) is a method to measure the maximum loss with a certain level of confidence in a certain period. Monte Carlo simulation is the most popular method of calculating VaR. The purpose of this study is to demonstrate control variates method as a variance reduction method that can be applied to estimate VaR. Moreover, it is to compare the results with the normal VaR method or analytical VaR calculation. Control variates method was used to find new returns from all stocks which are used as estimators of the control variates. The new returns were then used to define parameters needed to generate N random numbers. Furthermore, the generated numbers were used to find the VaR value. The method was then applied to estimate a portfolio of the game and esports company stocks that are EA, TTWO, AESE, TCEHY, and ATVI . The results show Monte Carlo simulation gives VaR of US$41.6428 within 1000 simulation, while the analytical VaR calculation  or  normal VaR method gives US$30.0949.

Junyu Zhang ◽  
Lin Xiao ◽  
Shuzhong Zhang

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for nonconvex optimization because of its capability of finding an approximate local solution with a second order guarantee and its low iteration complexity. Several recent works extend this method to the setting of minimizing the average of N smooth functions by replacing the exact gradients and Hessians with subsampled approximations. It is shown that the total Hessian sample complexity can be reduced to be sublinear in N per iteration by leveraging stochastic variance reduction techniques. We present an adaptive variance reduction scheme for a subsampled Newton method with cubic regularization and show that the expected Hessian sample complexity is [Formula: see text] for finding an [Formula: see text]-approximate local solution (in terms of first and second order guarantees, respectively). Moreover, we show that the same Hessian sample complexity is retained with fixed sample sizes if exact gradients are used. The techniques of our analysis are different from previous works in that we do not rely on high probability bounds based on matrix concentration inequalities. Instead, we derive and utilize new bounds on the third and fourth order moments of the average of random matrices, which are of independent interest on their own.

2021 ◽  
Vol 32 (11) ◽  
Qing-Quan Pan ◽  
Teng-Fei Zhang ◽  
Xiao-Jing Liu ◽  
Hui He ◽  
Kan Wang

2021 ◽  
Vol 9 ◽  
Salvador García-Pareja ◽  
Antonio M. Lallena ◽  
Francesc Salvat

After a brief description of the essentials of Monte Carlo simulation methods and the definition of simulation efficiency, the rationale for variance-reduction techniques is presented. Popular variance-reduction techniques applicable to Monte Carlo simulations of radiation transport are described and motivated. The focus is on those techniques that can be used with any transport code, irrespective of the strategies used to track charged particles; they operate by manipulating either the number and weights of the transported particles or the mean free paths of the various interaction mechanisms. The considered techniques are 1) splitting and Russian roulette, with the ant colony method as builder of importance maps, 2) exponential transform and interaction-forcing biasing, 3) Woodcock or delta-scattering method, 4) interaction forcing, and 5) proper use of symmetries and combinations of different techniques. Illustrative results from analog simulations (without recourse to variance-reduction) and from variance-reduced simulations of various transport problems are presented.

2021 ◽  
Vol 14 (11) ◽  
pp. 504
François-Michel Boire ◽  
R. Mark Reesor ◽  
Lars Stentoft

Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.

2021 ◽  
Zeljko Kereta ◽  
Robert Twyman ◽  
Simon R Arridge ◽  
Kris Thielemans ◽  
Bangti Jin

2021 ◽  
Jackson Morgan ◽  
Alex Long ◽  
Kendra Long

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