Variational variance reduction for particle transport eigenvalue calculations using Monte Carlo adjoint simulation

Second-order sensitivity and uncertainty analysis of the Roussopoulos-functional for a subcritical multiplying nuclear system with source

With large-scale wind farms integrated into power systems, the computational requirements for reliability evaluation of composite power systems are increasing. This paper introduces a new concept of dynamic orthogonal list, which is a form of multiple failure retrievals to avoid repeatedly calling the optimal power flow (OPF) program in the stage of state evaluation. An existing algorithm of cross-entropy (CE) method was developed to deal with the rare events in sampling. The major contribution of CE is to achieve convergence faster and reduce the number of samples, thus shortening the consuming time in the stage of sampling. This paper proposes a fast reliability evaluation process which combines the CE method with dynamic orthogonal list (CE-DOL), comprehensively improving the computational efficiency of Monte Carlo simulation (MCS). The proposed method is tested on a modified IEEE-RTS 79 system. In addition, for comparison purposes, the efficiencies of MCS, CE, and CE-DOL are estimated in the cases of different system adequacies. It is shown that, in range of certain reliability level, the proposed method is much more efficient compared with the CE method. Finally, the applicability of different methods is analyzed under different system reliability levels.

This study presents an efficient Monte Carlo simulation method to solve multivariate uncertainty problems in structural dynamic systems. The full model is obtained by the adaptive time-step material point method, and the multivariate surrogate model is built and analyzed for uncertainty by the adaptive sparse polynomial chaos expansion. The cubic spline interpolation method serves as a bridge between the original full model and the multivariate surrogate model, which improves the sampling efficiency of Monte Carlo simulation. Numerical results show that the proposed algorithm can significantly improve the efficiency and accuracy of uncertainty analysis.

A sample-efficient deep learning method for multivariate uncertainty qualification of acoustic–vibration interaction problems

This paper proposes three new advanced techniques for engineering reliability analysis. These are computational tools that interface with the physical behavior model of the system and use the statistical information about the primitive random variables to estimate the reliability. Three types of strategies have been used for such computation: analytical methods, response surface methods, and Monte Carlo simulation. All three strategies are improved for efficiency and accuracy with the proposed techniques. In the case of analytical methods, a multiple linear approximation of the limit state is proposed for the reliability estimation of highly nonlinear problems. For problems with large computational models, response surface approximation may be expensive. An alternative approach based on the kriging technique is proposed to overcome this hurdle. Similarly, the efficiency of Monte Carlo simulation is greatly improved by the use of an adaptive importance sampling technique.

Global variance reduction method based on multi-group Monte Carlo adjoint calculation

This study explores a hybrid method to enhance the efficiency of Monte Carlo simulations for European option pricing by incorporating neural network models. Traditional Monte Carlo Methods require high computational costs when dealing with high-dimensional financial derivatives due to the increased demand for simulation paths to achieve prediction accuracy. By integrating a feedforward neural network, this research aims to predict future price paths based on intermediate simulations, effectively reducing the number of paths while maintaining pricing accuracy. The proposed model employs residual block, regularization, early stopping, and other techniques to capture the nonlinear relationships between price paths and payoffs. Based on the trained model, the number of simulation paths required is successfully reduced from 10,000 to around 4,000 5,000 without significantly reducing prediction accuracy while achieving a balance in computation costs. The method exhibits stable predictive performance and computational efficiency, providing a potential solution for reducing the overhead of pricing complex financial derivatives. Future work could explore more advanced neural network architectures and hybrid with other techniques to further improve performance and efficiency.

Rare event simulation in the context of queueing networks has been an active area of research for more than two decades. A commonly used technique to increase the efficiency of Monte Carlo simulation is importance sampling. However, there are few rigorous results on the design of efficient or asymptotically optimal importance sampling schemes for queueing networks. Using a recently developed game/subsolution approach, we construct simple and efficient state-dependent importance sampling schemes for simulating buffer overflows in stable open Jackson networks. The sampling distributions do not depend on the particular event of interest, and hence overflow probabilities for different events can be estimated simultaneously. A by-product of the analysis is the identification of the minimizing trajectory for the calculus of variation problem that is associated with the sample-path large deviation rate function.

This chapter develops methods for increasing the efficiency of Monte Carlo simulation by reducing the variance of simulation estimates. These methods draw on two broad strategies for reducing variance: taking advantage of tractable features of a model to adjust or correct simulation outputs, and reducing the variability in simulation inputs. We discuss control variates, antithetic variates, stratified sampling, Latin hypercube sampling, moment matching methods, and importance sampling, and we illustrate these methods through examples. Two themes run through this chapter: The greatest gains in efficiency from variance reduction techniques result from exploiting specific features of a problem, rather than from generic applications of generic methods. Reducing simulation error is often at odds with convenient estimation of the simulation error itself; in order to supplement a reduced-variance estimator with a valid confidence interval, we sometimes need to sacrifice some of the potential variance reduction. KeywordsImportance SamplingVariance ReductionLatin Hypercube SamplingGeometric Brownian MotionUnderlying AssetThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

Aiming at the low efficiency of Monte Carlo simulation in power system probability analysis. The paper will use layered important sampling technology in reliability evaluation. The system state space is divided into different levels of subspace according to the important degree and category of system components. It will calculate the optimal multipliers of failure probability in the different layers and optimize the important sampling function gradually. So the later algorithm will have more advantage .It avoids the degeneration phenomenon for conventional sampling in the higher reliability system. The paper compared the method of this paper whit other methods in IEEE-RTS79 and its modified system. The results show the method of this paper not only ensuring calculation accuracy but also improving the calculation speed and efficiency.

This chapter presents methods for pricing options using the Monte Carlo approach. To provide tools for simulation, the chapter starts with methods for integrating stochastic differential equations. Illustrated with European-type options, a basic Monte Carlo approach is explained, together with methods of variance reduction (antithetic and control variates). Monte Carlo is applied to a two-asset binary put. Then the chapter describes two Monte Carlo approaches for American-style options, namely, parametric methods and regression methods. The chapter ends with the calculation of sensitivities such as Greeks. Pathwise sensitivities and the adjoint method are introduced.KeywordsMonte Carlo SimulationMonte CarloWiener ProcessAmerican OptionMonte Carlo ApproachThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nowadays, there is a problem of a lack of computer power to conduct high-precision reactor analysis. There are several factors that increase the excessive computational load and make it difficult to calculate nuclear reactor full-scale models using Monte Carlo method. Among them is the large neutron-flux attenuation, which is observed in deep penetration problems. Various reduction techniques are used to increase the efficiency of Monte Carlo calculations in such tasks. It allows to reduce the statistical uncertainty of the functional evaluation without increasing the number of neutron histories. This work is devoted to study and testing of variance reduction techniques in the deep penetration problem. To demonstrate the possibility of using non-analogue Monte Carlo modeling a test problem was formulated. To quantify the efficacy of applying the variance reduction methods, FOM characteristic is considered, which is a function of the relative error in a flux estimate and the computational time of the simulation. The article considers non-analogue techniques implemented in the MCU (Monte Carlo Univarsal) and OpenMC codes. As part of the study, a module of the OpenMC code was developed that allows to automatically generate weight windows. It is shown that variance reduction techniques increase the calculation efficiency by several times, particularly, the weight windows method in OpenMC make it possible to achieve a 7-fold increase in the efficiency of neutron flux estimation with the same number of simulated histories. The formulated recommendations can be used in the calculation of innovative nuclear reactors full-scale models.

The design of prompt-gamma detectors necessitates numerous Monte Carlo simulations to precisely develop and optimize the detection stages in proton therapy. Alongside the advancement of MC simulations, various variance reduction methods have been explored to speed-up calculations. Among these techniques, track-length estimators are interesting scoring methods for achieving both speed and accuracy in Monte Carlo simulations of rare events. This paper introduces an extension of the GATE vpgTLE module that incorporates the prompt-gamma emission time, which is tagged from the proton tracking, enhancing its utility for studies focused on detector design and optimization that rely on time measurements. The results obtained from a clinical radiotherapy plan are presented. We demonstrate that the new vpgTLE tally with time tagging is accurate, except for certain prompt-gamma lines corresponding to long mean-life nuclei.

Pricing derivatives written on assets whose prices depend on multiple factors can be difficult, even if payoffs depend only on prices at maturity. In complicated problems, Monte Carlo simulation is a popular technique, but it can be time-consuming when accuracy is needed. Conditional Monte Carlo is a known variance reduction method, but its use has been limited by a presumption in the literature that it can be used only when factors are instantaneously uncorrelated. I show that this presumption is not necessarily true. For example, we can express the prices and sensitivities of an European call option written on an asset that has stochastic volatility as an expectation over its Black-Scholes counterparts, even when the volatility and price processes exhibit instantaneous correlation. Combining this conditional Monte Carlo technique with low-discrepancy ("quasi-random") techniques provides price and delta estimators that require a fraction of a second to compute and yet have exact errors that are accurate to a few one-hundredths of a percent of the option's price. By comparison, conventional Monte Carlo simulation requires at least several minutes of computation time to achieve the same accuracy.