Efficiency Of Monte Carlo Simulation Research Articles

Extension of K-nearest neighbors and introduction of an applicable prediction criterion for a novel Monte Carlo simulation-based method in structural reliability

Efficiency is an important issue in structural reliability analysis. In this paper, a novel method is proposed to increase the efficiency of Monte Carlo Simulation by means of a machine learning algorithm. Using K-nearest neighbors method, the safe or failure region of many generated samples can be predicted without evaluating the limit state function. The proposed method represents three novel parts as its main core. In the first part of the proposed method, the classical K-nearest neighbors algorithm has been extended to a new fuzzy level such that the proposed method could predict even if all K neighbors are not in the same region. In previous similar methods, there is a prerequisite that K neighbors must be all in the failure region or all in the safe region. This extension to the fuzzy level is carried out by assigning a specific failure weight to each neighbor. In the second part of the proposed method, an innovative diagnostic criterion has been defined to check whether the region of a sample could be predicted or the sample has to be evaluated in the limit state function. The criterion describes the relative position of the newly generated sample with respect to the neighbors. This newly defined criterion is an effective alternative for the laborious action of drawing the convex hull around K neighbors, which is done as a time-consuming part in previous similar methods. Promotion of the accuracy or efficiency in the proposed method could be set using the adjusting parameter of the represented criterion. Since the implementation of the algorithm for each individual sample needs much time, in the third part, the proposed method introduces a technique to perform function evaluations or predictions in clusters. This part effectively reduces the computational burden, i.e. the number of function evaluations and run time. The performance of the proposed method, applying three novel and newly represented parts, has been verified using a number of mathematical and structural examples.

An automation of Monte Carlo workflow for dosimetry study of an Elekta LINAC delivery system in radiotherapy

PurposeThis study aims to automate the Monte Carlo (MC) workflow utilized for radiotherapy dosimetry, focusing on an Elekta LINAC delivery system. It addresses the challenge of integrating MC simulations into routine clinical practice, making this accurate yet complex method more accessible and efficient for radiotherapy dosimetry. Methods and MaterialsWe developed a user-friendly software featuring a graphical user interface (GUI) that integrates EGSnrc for MC simulations. The software streamlines the process from retrieving Digital Imaging and Communications in Medicine (DICOM) data to executing dose calculations and comparing dose distributions. To validate our proposed tool, we compared its computed doses for IMRT and VMAT plans from the Pinnacle TPS for an Elekta Versa HD linear accelerator against MC simulation results. This comparison utilized our in-house software and GUI as the tool, covering various treatment sites and prescriptions. ResultsThe automated MC workflow demonstrated high accuracy in dose calculations and streamlined integration with clinical workflows. The comparison between the MC-simulated and TPS-calculated doses revealed excellent agreement, highlighting the reliability of MC for independent dose verification in complex treatment scenarios. ConclusionsThe automated MC workflow developed represents a substantial improvement in the practicality and efficiency of MC simulations in radiotherapy. This advancement not only simplifies the dosimetry process but also ensures high accuracy, establishing it as a valuable tool for routine patient-specific quality assurance and the development of specialized treatment procedures.

Decay Dose Shielding Analysis with Hybrid Unstructured Mesh/Constructive Solid Geometry Monte Carlo Calculation and ADVANTG Acceleration

The target segments of the Oak Ridge National Laboratory Second Target Station (STS) neutron production facility become highly activated due to spallation reactions or nuclei transmutation by primary protons and emitted neutrons. Once the target segments are removed from their location within the core vessel, decay dose rates must be accurately quantified to determine the shielding configurations of remote-handling tools and transport casks and to aid in planning maintenance activities. For this analysis, we utilized a hybrid unstructured mesh (UM)/constructive solid geometry approach for calculating spallation products and neutron fluxes, activation calculations using the AARE package that includes the CINDER2008 activation code to calculate the decay photon source at different cooling times, and the ADVANTG code to accelerate the final decay photon transport calculation. Both Type 316 stainless steel (SS-316) and lead were investigated as candidates for shielding materials. The decay photon transport calculation through the thick SS-316 or lead shields exhibited between 25 and 30 orders-of-magnitude attenuations in the radial direction, depending on the shield. Such a difficult shielding calculation required advanced variance reduction. ADVANTG has some missing features, which limits its usability in spallation neutron source applications. It does not support volumetric sources created for MCNP6.2 UM capability. An approximate source was created for this problem. Not only was this approximate source needed for running the ADVANTG calculation to generate the weight windows, but also it was essential to develop source biasing (SB) parameters that were crucial for dramatically accelerating the decay photon transport in this problem. With this approximate source, the analysis was completed in a very reasonable computational time, and the design of the STS remote-handling equipment was finalized. This paper compares the efficiency of Monte Carlo simulations with different weight window and SB parameters calculated using different approximate ADVANTG calculations.

Quantifying tissue optical properties of human heads in vivo using continuous-wave near-infrared spectroscopy and subject-specific three-dimensional Monte Carlo models.

.Significance: Quantifying subject-specific optical properties (OPs) including absorption and transport scattering coefficients of tissues in the human head could improve the modeling of photon propagation for the analysis of functional near-infrared spectroscopy (fNIRS) data and dosage quantification in therapeutic applications. Current methods employ diffuse approximation, which excludes a low-scattering cerebrospinal fluid compartment and causes errors.Aim: This work aims to quantify OPs of the scalp, skull, and gray matter in vivo based on accurate Monte Carlo (MC) modeling.Approach: Iterative curve fitting was applied to quantify tissue OPs from multidistance continuous-wave NIR reflectance spectra. An artificial neural network (ANN) was trained using MC-simulated reflectance values based on subject-specific voxel-based tissue models to replace MC simulations as the forward model in curve fitting. To efficiently generate sufficient data for training the ANN, the efficiency of MC simulations was greatly improved by white MC simulations, increasing the detectors’ acceptance angle, and building a lookup table for interpolation.Results: The trained ANN was six orders of magnitude faster than the original MC simulations. OPs of the three tissue compartments were quantified from NIR reflectance spectra measured at the forehead of five healthy subjects and their uncertainties were estimated.Conclusions: This work demonstrated an MC-based iterative curve fitting method to quantify subject-specific tissue OPs in-vivo, with all OPs except for scattering coefficients of scalp within the ranges reported in the literature, which could aid the modeling of photon propagation in human heads.

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

We propose an efficient Monte Carlo simulation method to address the multivariate uncertainties in acoustic–vibration interaction systems. The deep neural network acts as a general surrogate model to enhance the sampling efficiency of Monte Carlo Simulation. Singular Value Decomposition - Radial Basis Functions (SVD-RBF) acts as a bridge between the original full model and the neural network, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The snapshots of full order models are obtained with isogeometric analysis, in which we couple two numerical schemes for vibro–acoustic interaction problems: the isogeometric finite element method for simulating vibration of Kirchhoff–Love shells and isogeometric boundary element method for exterior acoustic waves. Numerical results show that the proposed algorithm can significantly improve the efficiency of uncertainty analysis.

Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles.

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.

Reliability Evaluation of Composite Power Systems Considering Wind Farms Based on Cross Entropy and Dynamic Orthogonal List

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.

Monte Carlo Simulation and Improvement of Variance Reduction Techniques

Variance reduction technique is an important method to improve the efficiency of Monte Carlo simulation. In order to research the principle of reducing variance, we introduce Monte Carlo simulation firstly; then enumerate several commonly used methods of variance reduction and furtherly combine them to study whether it improves the simulation performance; lastly, we write programs to compare the reduction rates of different methods on the same problem. It turns out that variance reduction techniques have remarkable effect on increasing the calculation accuracy and reducing the calculation time of Monte Carlo simulation. And the combination of multiple variance reduction techniques is more effective in practical application.

Variance Reduction and Efficiency of Monte Carlo Simulation in Financial Model

In recent years, finance specialists have described several phenomena and they are developing calculation methods thanks to mathematical tools that are becoming more and more sophisticated. Thus, our research aims to use in a practical way the main operating techniques of the Monte Carlo simulation applied to finance. This article presents the Monte Carlo method as part of the simulation of the stochastic model in finance. Note that the use of this method often represents an extra cost in calculation that should be taken into account in the study of performance. Indeed, the method is not effective when the variance is too high. A technique of variance reduction is the solution to reduce the variability of the estimators and consequently reduce the simulation time. A reduction of the variance can only be accomplished by means of knowledge of information, which can be quantitative or qualitative on the studied phenomenon. The more information we have, the lower the variability of the estimator is likely to be.

Fast reliability evaluation method for composite power system based on the improved EDA and double cross linked list

To improve the computational efficiency of Monte Carlo simulation in composite power systems reliability evaluation, this study presents a method based on the improved estimation of distribution algorithm (EDA) and double cross linked list. Compared to traditional techniques, this method is comprehensively improved in the stage of both sampling and state evaluation. In the sampling stage, the population-based incremental learning algorithm is presented, where the probability vector is updated based on the distribution characteristics of excellent samples in population of previous generations. Meanwhile, setting a limit to the probabilities of elements in normal state and mutation strategy are introduced, which improves the excellent characteristics of the population. In the state evaluation stage, the state search and match process is speed up by utilising the intelligent storage technology based on the double across linked list. It avoids calling the optimal power flow for the same state repeatedly. Finally, the proposed method is tested in IEEE RTS 79. As the result shows, compared with other methods ever used in reliability evaluation, this method is not only more efficient in computation but also more accurate. Thus, the proposed method is proved to be reliable and effective.

A variance reduction technique for long-term fatigue analysis of offshore structures using Monte Carlo simulation

Long-term fatigue assessment of an offshore structure is a challenging practical problem. An offshore structure is exposed to fluctuating sea conditions, thus the fatigue analysis needs to account for many different wave heights and periods. Because each sea state entails a full dynamic analysis, the total computational effort can be formidable, particularly for time domain analysis. Recently, researchers have proposed various strategies for efficient estimation of the long-term mean damage, but these methods all have drawbacks, such as the predicted damage is approximate without means to quantify the error, and the simulation procedure is customized for a particular stress location. This paper outlines a new approach based on using control variates to enhance the efficiency of Monte Carlo simulation. The proposed approach has the advantage of being a post-processing scheme that does not alter the dynamic simulation procedure, enabling the damage of multiple locations to be evaluated from the same simulation results. The predicted mean damage is unbiased and the sampling error can be quantified. In addition, the approach supports both time domain and frequency domain analysis. Case studies of a floating production system demonstrate that the proposed approach provides a substantial speedup in computational time. The actual performance varies with factors such as sample size and model complexity.

DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming

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.

Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence

Surrogate model methods are attractive ways to improve the efficiency of Monte Carlo simulation (MCS) for structural reliability analysis. An intelligent surrogate model based method for slope system reliability analysis is presented in this study. The novel machine learning technique ν-support vector machine (ν-SVM) is adopted to establish the surrogate model to predict the factor of safety via the samples generated by Latin hypercube sampling. Global optimization algorithms particle swarm optimization and artificial bee colony algorithm are adopted to select the hyper-parameters of ν-SVM model. The applicability of the ν-SVM based surrogate model for slope system reliability analysis is tested on four examples with obvious system effects. It is found that the proposed surrogate model combined with MCS can achieve accurate system failure probability evaluation using fewer deterministic slope stability analyzes than other approaches.

Improved efficiency in Monte Carlo simulation for passive-scattering proton therapy

The aim of this work was to improve the computational efficiency of Monte Carlo simulations when tracking protons through a proton therapy treatment head. Two proton therapy facilities were considered, the Francis H Burr Proton Therapy Center (FHBPTC) at the Massachusetts General Hospital and the Crocker Lab eye treatment facility used by University of California at San Francisco (UCSFETF). The computational efficiency was evaluated for phase space files scored at the exit of the treatment head to determine optimal parameters to improve efficiency while maintaining accuracy in the dose calculation.For FHBPTC, particles were split by a factor of 8 upstream of the second scatterer and upstream of the aperture. The radius of the region for Russian roulette was set to 2.5 or 1.5 times the radius of the aperture and a secondary particle production cut (PC) of 50 mm was applied. For UCSFETF, particles were split a factor of 16 upstream of a water absorber column and upstream of the aperture. Here, the radius of the region for Russian roulette was set to 4 times the radius of the aperture and a PC of 0.05 mm was applied. In both setups, the cylindrical symmetry of the proton beam was exploited to position the split particles randomly spaced around the beam axis.When simulating a phase space for subsequent water phantom simulations, efficiency gains between a factor of 19.9 ± 0.1 and 52.21 ± 0.04 for the FHTPC setups and 57.3 ± 0.5 for the UCSFETF setups were obtained. For a phase space used as input for simulations in a patient geometry, the gain was a factor of 78.6 ± 7.5. Lateral-dose curves in water were within the accepted clinical tolerance of 2%, with statistical uncertainties of 0.5% for the two facilities. For the patient geometry and by considering the 2% and 2mm criteria, 98.4% of the voxels showed a gamma index lower than unity. An analysis of the dose distribution resulted in systematic deviations below of 0.88% for 20% of the voxels with dose of 20% of the maximum or more.

Efficiency of Monte Carlo sampling in chaotic systems.

In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.

Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions

Recently, Velazquez and Curilef proposed a methodology to extend Monte Carlo algorithms based on a canonical ensemble which aims to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions. We show in this work that Monte Carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point. Our study is performed for the particular case of a two-dimensional four-state Potts model on a square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sampling is more efficient than the usual Swendsen-Wang and Wolff cluster algorithms. These results demonstrate the effectiveness of this methodology to improve the efficiency of MC simulations of systems that undergo any type of temperature-driven phase transition.

Importance sampling and statistical Romberg method

The efficiency of Monte Carlo simulations is significantly improved when implemented with variance reduction methods. Among these methods, we focus on the popular importance sampling technique based on producing a parametric transformation through a shift parameter $\theta$. The optimal choice of $\theta$ is approximated using Robbins–Monro procedures, provided that a nonexplosion condition is satisfied. Otherwise, one can use either a constrained Robbins–Monro algorithm (see, e.g., Arouna ( Monte Carlo Methods Appl. 10 (2004) 1–24) and Lelong ( Statist. Probab. Lett. 78 (2008) 2632–2636)) or a more astute procedure based on an unconstrained approach recently introduced by Lemaire and Pages in ( Ann. Appl. Probab. 20 (2010) 1029–1067). In this article, we develop a new algorithm based on a combination of the statistical Romberg method and the importance sampling technique. The statistical Romberg method introduced by Kebaier in ( Ann. Appl. Probab. 15 (2005) 2681–2705) is known for reducing efficiently the complexity compared to the classical Monte Carlo one. In the setting of discritized diffusions, we prove the almost sure convergence of the constrained and unconstrained versions of the Robbins–Monro routine, towards the optimal shift $\theta^{*}$ that minimizes the variance associated to the statistical Romberg method. Then, we prove a central limit theorem for the new algorithm that we called adaptive statistical Romberg method. Finally, we illustrate by numerical simulation the efficiency of our method through applications in option pricing for the Heston model.

Increasing the efficiency of Monte Carlo simulation with sampling from an approximate potential

Nested Markov Chain Monte Carlo (MCMC) simulation using two potential functions, where the move for MCMC with one potential function (primary chain) is given by a short MCMC run with the other potential function (auxiliary chain) is well known. However, generally the acceptance of these moves is low. In this work, a scheme has been developed to increase the acceptance rate and applied to (H2O)20 and (H2O)25, where the primary and auxiliary chains are represented by a quantum mechanical (QM) and a classical potential respectively. A comparison between standard and nested MC simulation for (H2O)4 showed impressive results.

Multidimensional B-spline parameterization of the detection probability of PET systems to improve the efficiency of Monte Carlo simulations

Accurate modeling of system response and scatter distribution is crucial for image reconstruction in emission tomography. Monte Carlo simulations are very well suited to calculate these quantities. However, Monte Carlo simulations are also slow and many simulated counts are needed to provide a sufficiently exact estimate of the detection probabilities. In order to overcome these problems, we propose to split the simulation into two parts, the detection system and the object to be imaged (the patient). A so-called ‘virtual boundary’ that separates these two parts is introduced. Within the patient, particles are simulated conventionally. Whenever a photon reaches the virtual boundary, its detection probability is calculated analytically by evaluating a multi-dimensional B-spline that depends on the photon position, direction and energy. The unknown B-spline knot values that define this B-spline are fixed by a prior ‘pre-’ simulation that needs to be run once for each scanner type. After this pre-simulation, the B-spline model can be used in any subsequent simulation with different patients. We show that this approach yields accurate results when simulating the Biograph 16 HiREZ PET scanner with Geant4 Application for Emission Tomography (GATE). The execution time is reduced by a factor of about 22 × (scanner with voxelized phantom) to 30 × (empty scanner) with respect to conventional GATE simulations of same statistical uncertainty. The pre-simulation and calculation of the B-spline knots values could be performed within half a day on a medium-sized cluster.

Expected-value techniques for Monte Carlo modeling of well logging problems

This article describes research performed to develop an expected-value (EV) estimation capability for improving the efficiency of Monte Carlo simulations of oil well logging problems. The basic idea underlying EV estimation is that event-level interaction and transport probabilities are known and can be averaged exactly to produce unbiased estimators that properly account for potential future events in the simulation. Conventional surface-crossing and track-length based estimators do not provide any information unless a particle history actually reaches a detector region. Expected-value estimators, however, can extract information from particles that merely travel along a direction intercepting the detector region. This paper describes two expected-value estimators that have been developed for oil well logging simulations. The first estimates the volume-averaged scalar flux or reaction rate in a detector. The second estimates a weighted surface-averaged incident current that can be enfolded with a detector response function to estimate pulse-height spectra. Though EV estimation reduces variance at the event level, it does not guarantee reduced variance at the history level. However, our oil well logging tests indicate that the EV approach generally improves information content, enhances the efficiency of the transport simulation, and provides an efficient technique to obtain the fluxes, reaction rates, and pulse-height spectra in detectors, especially when applied in conjunction with weight-window variance reduction techniques.