Correlated Sampling Technique Research Articles

Sensitivity and perturbation analysis of alpha-eigenvalue with time-dependent Monte Carlo perturbation techniques

Sensitivity analysis and perturbation calculation methods for prompt neutron decay constants α using the Monte Carlo method, such as iterative fission probability (IFP), differential operator sampling (DOS), and correlated sampling (CS), have been proposed thus far. However, these methods require a significant amount of memory storage. The method developed in this study applies DOS and CS techniques during a time-dependent Monte Carlo simulation for the pulsed neutron method in subcritical systems. The time variation of the neutron flux is fitted to an exponential function during the time range when the flux decays with the fundamental mode α. By applying the least squares method to the results of time-dependent DOS and CS, the sensitivity coefficients with respect to nuclear data and the change in α due to perturbation can be calculated. In contrast to the existing methods that require storing the total fission or time sources per generation over several (∼10) generations, the proposed method only needs to store the weighting coefficient of a single source particle until it dies. The additional memory storage per parameter is comparable to that of conventional time-dependent Monte Carlo simulations and much less than that of existing methods. Numerical tests for the proposed method have demonstrated the accuracy and usefulness of the time-dependent DOS and CS methods.

Tool Developments in the OpenMC Code: Correlated Sampling and Transient Fission Matrix Approach Coupled to OpenFOAM

This article outlines the advancements made in broadening the application scope of the OpenMC neutron transport code to include thermohydraulic coupling and nuclear data uncertainty propagation. These developments primarily involve the incorporation of the correlated sampling (CS) technique, facilitating the propagation of thermal feedback or cross-section sampling on neutronic calculations through neutron weight adjustments. The CS technique is integrated with computer-aided-design (CAD)–based meshing and the Transient Fission Matrix (TFM) approach. Together, these components enable comprehensive handling of neutronics-thermohydraulic coupling: The TFM approach addresses neutron kinetics via precalculated neutron transport matrices, the CS technique accounts for thermal feedback impacts on the matrices, and CAD meshing defines volumes corresponding to each matrix bin to align results with computational fluid dynamics codes, specifically OpenFOAM. Implementation details and verification procedures are elaborated, alongside an analysis on existing limitations and possible perspectives.

Ab initio molecular dynamics on quantum computers.

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann-Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.

Uncertainty propagation based on correlated sampling technique for nuclear data applications

A correlated sampling technique has been implemented to estimate the impact of cross section modifications on the neutron transport and in Monte Carlo simulations in one single calculation. This implementation has been coupled to a Total Monte Carlo approach which consists in propagating nuclear data uncertainties with random cross section files. The TMC-CS (Total Monte Carlo with Correlated Sampling) approach offers an interesting speed-up of the associated computation time. This methodology is detailed in this paper, together with two application cases to validate and illustrate the gain provided by this technique: the highly enriched uranium/iron metal core reflected by a stainless-steel reflector HMI-001 benchmark, and the PETALE experimental programme in the CROCUS zero-power light water reactor.

Uncertainty propagation for the design study of the PETALE experimental programme in the CROCUS reactor

The PETALE experimental programme in the CROCUS reactor intends to provide integral measurements to constrain stainless steel nuclear data. This article presents the tools and the methodology developed to design and optimize the experiments, and its operating principle. Two acceleration techniques have been implemented in the Serpent2 code to perform a Total Monte Carlo uncertainty propagation using variance reduction and correlated sampling technique. Their application to the estimation of the expected reaction rates in dosimeters is also discussed, together with the estimation of the impact of the nuisance parameters of aluminium used in the experiment structures.

On Achieving High Accuracy in Quantum Chemical Calculations of 3 d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules.

The bond dissociation energies of a set of 44 3 d transition metal-containing diatomics are computed with phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing a correlated sampling technique. We investigate molecules with H, N, O, F, Cl, and S ligands, including those in the 3dMLBE20 database first compiled by Truhlar and co-workers with calculated and experimental values that have since been revised by various groups. In order to make a direct comparison of the accuracy of our ph-AFQMC calculations with previously published results from 10 DFT functionals, CCSD(T), and icMR-CCSD(T), we establish an objective selection protocol which utilizes the most recent experimental results except for a few cases with well-specified discrepancies. With the remaining set of 41 molecules, we find that ph-AFQMC gives robust agreement with experiment superior to that of all other methods, with a mean absolute error (MAE) of 1.4(4) kcal/mol and maximum error of 3(3) kcal/mol (parentheses account for reported experimental uncertainties and the statistical errors of our ph-AFQMC calculations). In comparison, CCSD(T) and B97, the best performing DFT functional considered here, have MAEs of 2.8 and 3.7 kcal/mol, respectively, and maximum errors in excess of 17 kcal/mol (for the CoS diatomic). While a larger and more diverse data set would be required to demonstrate that ph-AFQMC is truly a benchmark method for transition metal systems, our results indicate that the method has tremendous potential, exhibiting unprecedented consistency and accuracy compared to other approximate quantum chemical approaches.

Transient fission matrix approach for assessing complex kinetics behavior in the ZEPHYR ZPR coupled core configurations

CEA is currently working on a new ZPR called ZEPHYR (Zero power Experimental PHYsics Reactor), to be built on the Cadarache Center in the next decade. Its awaited experimental capacities should go well beyond traditional needs, and in particular extended possibilities to assess complex 3D kinetics. Transient calculations with accurate neutron kinetics models can be challenged by designing strongly spatially coupled to strongly spatially uncoupled cores with different kinetics constant. An innovative Monte Carlo Transient Fission Matrix (TFM) approach based on fission matrix interpolation model connected to correlated sampling technique has been implemented and applied to the ZEPHYR reference fast/thermal coupled configuration. The model takes into account the redistribution of the power in the core for spatial kinetics (SK) thanks to a local correlated sampling technique developed for this purpose. However, point Kinetics (PK) can be treated as well. The correlated model presented in this paper estimates the coupling coefficients or the influence on the neutron transport of a local variation of different parameters on integral quantities such as k-eff. A dedicated 1D benchmark demonstrates interesting features of this kind of coupled configurations for the validation of complex space-time kinetics transient experiments. A further work will extend this preliminary results to a 2D study case.

On coupling fluid plasma and kinetic neutral physics models

The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry. For the benchmark case, residuals decay with particle number and increase with grid size, indicating that they scale in a manner that is similar to the theoretical prediction for nonlinear bias error. Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme. The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation.

Local correlated sampling Monte Carlo calculations in the TFM neutronics approach for spatial and point kinetics applications

These studies are performed in the general framework of transient coupled calculations with accurate neutron kinetics models. This kind of application requires a modeling of the influence on the neutronics of the macroscopic cross-section evolution. Depending on the targeted accuracy, this feedback can be limited to the reactivity for point kinetics, or can take into account the redistribution of the power in the core for spatial kinetics. The local correlated sampling technique for Monte Carlo calculation presented in this paper has been developed for this purpose, i.e. estimating the influence on the neutron transport of a local variation of different parameters such as sodium density or fuel Doppler effect. This method is associated to an innovative spatial kinetics model named Transient Fission Matrix, which condenses the time-dependent Monte Carlo neutronic response in Green functions. Finally, an accurate estimation of the feedback effects on these Green functions provides an on-the-fly prediction of the flux redistribution in the core, whatever the actual perturbation shape is during the transient. This approach is also used to estimate local feedback effects for point kinetics resolution.

Towards spatial kinetics in a low void effect sodium fast reactor: core analysis and validation of the TFM neutronic approach

The studies presented in this paper are performed in the general framework of transient coupled calculations with accurate neutron kinetics models able to characterize spatial decoupling in the core. An innovative fission matrix interpolation model has been developed with a correlated sampling technique associated to the Transient Fission Matrix (TFM) approach. This paper presents a validation of this Monte Carlo based kinetic approach on sodium fast reactors. An application case representative of an assembly of the low void effect sodium fast reactor ASTRID is used to study the physics of this kind of system and to illustrate the capabilities provided by this approach. To validate the interpolation model developed, different comparisons have been performed with direct Monte Carlo and ERANOS deterministic S N calculations on spatial kinetics parameters (flux redistribution, reactivity estimation, etc.) together with point kinetics feedback estimations.

CST-based first order second moment method for probabilistic slope stability analysis

Correlated random variables are commonly involved in probabilistic slope stability analysis, such as reliability analysis of slopes with spatially variable soil properties. This paper proposes a simple Correlated Sampling Technique (CST) for generating samples of correlated random variables. The CST firstly produces correlated standard-normally distributed samples through linear combinations of independent standard-normally distributed samples. Correlated arbitrarily distributed samples can then be obtained by the Nataf transformation. The CST was combined with FOSM (named CST-based FOSM) for probabilistic slope stability analysis. The slope reliabilities of a single-layered cohesive soil slope and a high earth and rockfill dam were analyzed to illustrate the CST-based FOSM. These illustrative examples indicated that the CST-based FOSM can accurately estimate the slope reliability indices with considerably fewer simulations (especially in the case of low failure probability) compared with direct MCS, and the slope reliability was sensitive to the correlation of the strength parameters.

A fast correlated multiple sampling technique based on 12-bit SAR ADC with digital calibration for low-noise CMOS image sensor

A fast multiple correlated sampling technique based on successive approximation register analog-to-digital converter (SAR ADC) for low-noise CMOS image sensors is proposed in this paper. During the whole operation of the fast multiple correlated sampling, m-times samplings and conversions are achieved. The SAR ADC completes a full conversion in the first conversion and only converts lower M bits in the following conversions to decrease the total conversion time. The influences of three factors, the number of samplings, the number of bits converted in the repeated conversions and the resolution of ADC, on the fast multiple correlated sampling are analyzed in detail. A 12-bit SAR ADC with digital calibration based one bit redundancy to relieve the requirement of the capacitor mismatch is designed in the fast correlated multiple sampling technique. The proposed correlated multiple sampling technique is implemented and simulated through standard 180nm CMOS process. The SAR ADC achieves 72.55dB signal-to-noise-and-distortion ratio after digital calibration. The simulation results match the analysis well. Readout noise in CMOS image sensors can be reduced by the factor of m effectively with appropriate M based on the fast correlated multiple sampling technique. The total conversion time is decreased effectively, and it is only 10.9μs for 16 times fast correlated multiple sampling. The fast multiple correlated sampling technique based on SAR ADC is suitable for low-noise and high-speed CMOS image sensor.

Poster — Thur Eve — 21: Off‐axis dose perturbation effects in water in a 5 × 5 cm2 18 MV photon beam for the PTW microLion and Exradin A1SL ionization chambers

A PTW microLion liquid ionization chamber and an Exradin A1SL air‐filled ionization chamber have been modeled using the egs_chamber user code of the EGSnrc system to determine their perturbation effects in water in a 5 × 5 cm2 18 MV photon beam. A model of the Varian CL21EX linear accelerator was constructed using the BEAMnrc Monte Carlo code, and was validated by comparing measured PDDs and profiles from the microLion and A1SL chambers to calculated results that included chamber models. Measured PDDs for a 5 × 5 cm2 field for the microLion chamber agreed with calculations to within 1.5% beyond a depth of 0.5 cm, and the A1SL PDDs agreed within 1.0% beyond 1.0 cm. Measured and calculated profiles at 10 cm depth agreed within 1.0% for both chambers inside the field, and within 4.0% near the field edge. Local percent differences increased up to 15% at 4 cm outside the field. The ratio of dose to water in the absence of the chamber relative to dose in the chamber's active volume as a function of off‐axis distance was calculated using the egs_chamber correlated sampling technique. The dose ratio was nearly constant inside the field and consistent with the stopping power ratios of water to detector material, but varied up to 3.3% near the field edge and 5.2% at 4 cm outside the field. Once these perturbation effects are fully characterized for more field sizes and detectors, they could be applied to clinical water tank measurements for improved dosimetric accuracy.

Towards Correlated Sampling for the Fixed-Node Diffusion Quantum Monte Carlo Method

Most methods of quantum chemistry calculate total energies rather than directly the energy differences that are of interest to chemists. In the case of statistical methods like quantum Monte Carlo the statistical errors in the absolute values need to be considerably smaller than their difference. The calculation of small energy differences is therefore particularly time consuming. Correlated sampling techniques provide the possibility to compute directly energy differences by simulating the underlying systems with the same stochastic process. The smaller the energy difference the smaller its statistical error. Correlated sampling is well established in variational quantum Monte Carlo, but it is much more difficult to implement in diffusion quantum Monte Carlo because of the fixed node approximation. A correlated sampling formalism and a corresponding algorithm based on a transformed Schrödinger equation having the form of a Kolmogorov’s backward equation is derived. The numerical verification of the presented algorithm is given for the harmonic oscillator. The extension of the algorithm to electron structure calculations is discussed.

Monte Carlo Fuel Temperature Coefficient Estimation by an Adjoint-Weighted Correlated Sampling Method

It is very time-consuming to obtain a high-precision Monte Carlo (MC) estimate of the fuel temperature reactivity coefficient (FTC) through direct subtraction of two reactivity values from MC calculations at two different fuel temperatures. As an alternative to the direct subtraction MC estimate of the FTC, this paper presents a new method based on the adjoint-weighted correlated sampling technique. The new method translates the change in fuel temperature as the corresponding changes in both the microscopic cross sections and the transfer probabilities in scattering kernels described by the free gas model. The effectiveness of the new method is examined through continuous-energy MC neutronics calculations for pressurized water reactor pin cell and CANDU pressurized heavy water reactor lattice problems. The isotope-wise and reaction-type–wise contributions to the FTCs in the two problems are examined for two free gas models: the constant-cross-section and the resonance-cross-section models. It is demonstrated that the new MC method can predict the reactivity change due to fuel temperature variation as accurately as the conventional, more time-consuming direct subtraction MC method.

Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in Three Dimensions.

A fast method is developed for calculating the random phase approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix, and the trace is taken by a stochastic approach using random perturbation vectors. For a fixed statistical error in the total energy per electron, the method scales, at most, quadratically with the system size; however, in practice, due to self-averaging, it requires less statistical sampling as the system grows, and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. We find that the RPA correlation energies per electron are largely independent of the nanocrystal size. In addition, we show that a correlated sampling technique enables calculation of the energy difference between two slightly distorted configurations with scaling and a statistical error similar to that of the total energy per electron.

Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

AbstractThe influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures. To measure the influence of the variation of emission levels over the pollutants concentrations the Sobol’ global sensitivity indices are estimated using efficient techniques for small sensitivity indices to avoid the effect of loss of accuracy. Theoretical studies, as well as, practical computations are performed in order to analyze efficiency of various variance reduction techniques for computing small indices. The importance of accurate estimation of small sensitivity indices is analyzed. It is shown that the correlated sampling technique for small sensitivity indices gives reliable results for the full set of indices. Its superior efficiency is studied in details.

Calculation of effective delayed neutron fraction with Monte Carlo perturbation techniques

New methods are proposed to estimate the effective delayed neutron fraction β eff in Monte Carlo calculations: the eigenvalue methods jointly used with the differential operator sampling and correlated sampling techniques. In particular, the eigenvalue method with the differential operator sampling technique has a distinct feature that it theoretically gives an exact β eff value. To verify the proposed methods, Monte Carlo calculations are performed for several systems with simple geometry. It is found that the results obtained with the proposed methods agree with the reference deterministic results within sufficiently small statistical uncertainties. The indirect perturbed source effect must be taken into account to estimate an exact β eff value.

Efficiency improvements for ion chamber calculations in high energy photon beams

This article presents the implementation of several variance reduction techniques that dramatically improve the simulation efficiency of ion chamber dose and perturbation factor calculations. The cavity user code for the EGSnrc Monte Carlo code system is extended by photon cross-section enhancement (XCSE), an intermediate phase-space storage (IPSS) technique, and a correlated sampling (CS) scheme. XCSE increases the density of photon interaction sites inside and in the vicinity of the chamber and results-in combination with a Russian Roulette game for electrons that cannot reach the cavity volume-in an increased efficiency of up to a factor of 350 for calculating dose in a Farmer type chamber placed at 10 cm depth in a water phantom. In combination with the IPSS and CS techniques, the efficiency for the calculation of the central electrode perturbation factor Pcel can be increased by up to three orders of magnitude for a single chamber location and by nearly four orders of magnitude when considering the Pcel variation with depth or with distance from the central axis in a large field photon beam. The intermediate storage of the phase-space properties of particles entering a volume that contains many possible chamber locations leads to efficiency improvements by a factor larger than 500 when computing a profile of chamber doses in the field of a linear accelerator photon beam. All techniques are combined in a new EGSnrc user code egs_chamber. Optimum settings for the variance reduction parameters are investigated and are reported for a Farmer type ion chamber. A few example calculations illustrating the capabilities of the egs_chamber code are presented.

Correlated sampling techniques used in Monte Carlo simulation for risk assessment

Risk assessments in the nuclear industry heavily depend on the study of system availability/reliability and component importance. To do this study, the Monte Carlo simulation method is often a favorite selection since it involves no complex mathematical analysis, especially when systems are so complex or large that deterministic methods are difficult to solve. However, when the importance of components or the time behavior of availability/reliability of a system are required, running conventional Monte Carlo simulation alone can be very tedious and time-consuming. An integrated analysis technique that can be used to obtain the entire information efficiently and precisely in one calculation would be very desired by the system engineers. In this paper, we introduce the correlated sampling techniques to incorporate with conventional Monte Carlo simulation to save engineer's work as well as computing time.