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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Factors That Influence Variability in Stress-Drop Measurements Using Spectral Decomposition and Spectral-Ratio Methods for the 2019 Ridgecrest Earthquake Sequence

Stress drop is a fundamental parameter related to earthquake source physics, but is hard to measure accurately. To better understand how different factors influence stress-drop measurements, we compare two different methods using the Ridgecrest stress-drop validation data set: spectral decomposition (SD) and spectral ratio (SR), each with different processing options. Here, we also examine the influence of spectral complexity on source parameter measurement. Applying the SD method, we find that frequency bandwidth and time-window length could influence spectral magnitude calibration, while depth-dependent attenuation is important to correctly map stress-drop variations. For the SR method, we find that the selected source model has limited influence on the measurements; however, the Boatwright model tends to produce smaller standard deviation and larger magnitude dependence than the Brune model. Variance reduction threshold, frequency bandwidth, and time-window length, if chosen within an appropriate parameter range, have limited influence on source parameter measurement. For both methods, wave type, attenuation correction, and spectral complexity strongly influence the result. The scale factor that quantifies the magnitude dependence of stress drop show large variations with different processing options, and earthquakes with complex source spectra deviating from the Brune-type source models tend to have larger scale factor than earthquakes without complexity. Based on these detailed comparisons, we make a few specific suggestions for data processing workflows that could help future studies of source parameters and interpretations.

58 GEOSCIENCES↗
DOE OSTI2026

Improved Regional Moment Tensor Inversion for Moderately Large Earthquakes in the Western United States Using a 3D Earth Model Based on Full Waveform Tomography

The nature of seismic sources for moderately large (moment magnitude, M w 5.0–6.5) events are commonly characterized by their moment tensor (MT) solutions and obtained by inversion of regional distance (200–1600 km) long‐period (20–50 s) waveforms. Regional MT estimates are often calculated from average plane‐layered, one‐dimensional (1D) velocity models. However, 1D model calculations can produce misfits in the arrival times and waveform shapes that introduce errors, particularly at longer distances or for shorter periods, which are necessary for analyzing lower magnitude events. Approximate Earth models (e.g., 1D) representing broad areas may be inadequate, particularly in the crust and uppermost mantle of tectonically complex regions. In this study, we show how a three‐dimensional (3D) Earth model obtained from full waveform inversion tomography can improve waveform fits and decrease phase errors. We developed a platform and workflow to perform routine 3D MT inversions and inverted MTs for 25 earthquakes in the western United States and seven nuclear explosions using an average 1D and a recent 3D Earth model, WUS256 (Rodgers et al., 2022). Using the 3D model improves waveform fits (variance reduction and phase time shifts) compared with the 1D model, and the 3D MT solutions are stable across large distances. This study shows that 3D models obtained from full waveform tomography can improve MTs and source characterization especially at far regional distances (>800 km).

Geosciences↗
DOE OSTI2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Codebase release r1.4 for CoVVVR

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named COVVVR, which implements our approach in the VEGAS program. The improvements are quantified with several benchmark examples from the literature.

Shyamsundar, Prasanth↗
DOE OSTI2021

Verification of Combined VR Techniques, Derivation of Future Time Equation, and Integration of LLNL Pulsed Sphere V&V Suite [Slides]

To determine whether the combination of forced-collision and DXTRAN variance-reduction (VR) techniques is unbiased, and to gain insight into the operation of these techniques, proof that first-moment estimates from Monte Carlo simulations employing both techniques are unbiased is developed. A general background on the forced-collision and DXTRAN VR techniques and their combination is given. Proof of an unbiased simulation is outlined by showing the equivalence of the history score moment equations of simulations with these techniques in use. A report with detailed proof of this equivalence is available upon request. The derivation of the future time equation using a similar approach, as well as a summary of the addition of the LLNL Pulsed Sphere experiments to the MCNP verification and validation suite, is also briefly discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assessment of Tools for Molten Salt Reactor Dose Rate Calculations

This report discusses a preliminary assessment of the capabilities of current state-of-the-art stochastic codes Shift and MCNP6 to calculate the ex-core radiation dose rates for a simplified Molten Salt Reactor (MSR) model. The Monte Carlo code Shift has been under significant development in recent years at ORNL as part of the CASL program and is now supported by NEAMS. Originally, Shift was developed for LWR ex-core calculations but with dose rate and shielding calculations specifically requested by the NEAMS program’s MSR industry partners, the MSR Application Drivers team was tasked with assessing Shift for non-LWR applications. This was the first application of the Shift code for non-LWRs and the findings can be considered preliminary due to the activities occurring only over a 5-month period. Attractive features of Shift include massive parallelization and advanced automated variance reduction techniques such as CADIS and FW-CADIS.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

VERA User's Guide for Ex-core Applications

The Virtual Environment for Reactor Applications, or VERA, allows users to set up models to calculate time-dependent and fully coupled solutions for ex-core quantities of interest such as vessel and coupon fluence, and detector responses for multiple statepoints and cycles. MPACT and COBRA-TF together perform in-core transport calculations with temperature feedback while Shift performs the fluence and detector response calculations in the ex-core region. The in-core region is modeled using VERA’s native input format and the ex-core region is defined using Shift’s general geometry package, also known as Omnibus General Geometry. Fixed source ex-core calculations with Shift can be run in forward mode without advanced variance reduction (VR) methods, or with Consistent Adjoint Driven Importance Sampling (CADIS), which is an automated VR method. This document serves as a guide for setting up inputs, running ex-core calculations and post-processing the results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Using the Criticality Accident Alarm System modeling capabilities in SCALE [Slides]

The following is a summary of advice for CAAS modeling in SCALE. Refer to the SCALE Criticality Safety and Radiation Shielding training slides or to the SCALE manual for exact syntax. Use a mesh for the fission source that is the most adequate for the problem to solve (coarse/fine). Don’t spend unnecessary resources; simplify the model if it does not impact the final results of interest. Be careful to deactivate secondary fissions in MAVRIC or the calculation may never end. Check that k eff and $\overline{\upsilon}$ calculated results are logical. Between KENO and MAVRIC, cross section libraries, materials, geometry, and mesh grid can be the same or different. Iterative calculations are usually complex problems that need variance reduction. It will be hard to find the best solving parameters in the first attempt; expert judgement is needed. Check each step separately. Use Fulcrum to visualize fission source, mesh source, and spatial/energy distributions to find potential errors or impactful imprecisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Results and Responses for the 2022 User Forum Survey [Slides]

This presentation discusses the results of a MCNP user survey. Example of questions asked include: "Which MCNP particle types do you typically use?," "What sort of simulations do you run most often?," "Do you build the code?," "Which variance reduction methods do you use?," "Opinions on HDF5," with frequent discussions regarding each question.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Oktavian Modeling and Analysis with MCNP6.3 [Poster]

Project Goals: Apply MCNP6 variance reduction (VR) techniques to improve the Oktavian benchmark experiment calculations; Verify VR methods and electron transport with MCNP6.3 unstructured mesh (UM) geometry. All MCNP calculations in this poster are for mode n, p, e.

42 ENGINEERING↗
DOE OSTI2025

FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment (Final Report)

This report documents the FY25 Theory and Simulation Performance Target (TSPT) of developing an integrated modeling framework for fusion reactor design and assessment (FREDA). Over Q1-Q4, new capabilities were developed across both plasma and engineering domains and demonstrated on an example representation of a Compact Advanced Tokamak with a Dual Cooled Lead Lithium blanket. This represents a first-of-a-kind demonstration of coupled core-to-wall-to-engineering for a reactor. Self-consistent CESOL workflows were applied to provide core, pedestal, and SOL prediction; new modules were developed for energetic particle stability (FAR3D) and transport (TGLF-EP) analysis; and boundary plasma modeling (SOLPS-ITER, BOUT++/Hermes-3) was expanded to evaluate wall and divertor heat fluxes and interface with engineering thermal analysis. A parameterized CAD tool, TRACER, was expanded to generate medium-fidelity divertor, blanket, and coil geometries; OpenFOAM and Diablo workflows were applied for first-wall and divertor thermal analyses with helium cooling; and reduced-order models were created for high-mass-flux divertor cooling. Magnet multiphysics capabilities were verified between Elmer, Diablo, and a new MFEM-based solver, and workflows enable stress, thermal, and neutron-fluence analysis of TF coils with neutronics-driven heating. Nuclear and blanket analysis workflows were demonstrated, including tritium breeding, transport, and CFD-informed thermo-mechanical assessment. Preliminary multi-fidelity uncertainty quantification workflows were applied to boundary modeling codes and shown to achieve variance reductions with fewer high-fidelity boundary simulations. Key findings highlight the challenges of resolving the ITEP gap to find suitable balance between wall and divertor loads, neutron heating, and practical limits of PFC cooling. Next step priorities are to develop automated workflows to check boundary code convergence and detachment, implement tighter physics-engineering CAD provenance tracking, and inclusion of plasma-material interface models for SLAG and tungsten cracking behavior. Collectively, these developments establish sophisticated capabilities for predictive, multi-fidelity, whole-device modeling that integrates plasma physics, materials, magnets, and nuclear engineering to guide pathways to viable Fusion Pilot Plant design points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

ACRRF High-Bay Dose Calculations using MCNP (Part A)

Analytical tools and models have been developed as a starting point for directly assessing dose in the Annular Core Research Reactor Facility (ACRRF) due to reactor operation. Key results include peak dose along the Central Cavity (CC) centerline (beamline) at the cavity level, dose throughout the High-Bay (HB), and dose on the facility roof for partially-shielded reactor operation where the 4” insert is removed from the CC Shield Plug (SP). Model results in the beamline are benchmarked against measured doses from passive dosimetry evaluations. Personnel total (neutron and gamma) dose in the ACRRF HB is calculated using Monte Carlo N-Particle (MCNP). Various CC and SP configurations are analyzed, including unshielded (no SP) and partially shielded (SP installed but 4” insert removed). Novel application of Variance Reduction (VR) techniques, namely the Surface Source Write (SSW) and Surface Source Read (SSR) capabilities in MCNP, enable impressive resolution (in a Monte Carlo modeling sense) of dose throughout much the facility. The VR techniques reduce stochastic error for challenging tallies, with more advanced techniques explored in the companion to this report (Part B) [1]. Supplementary studies (including a verification analysis) and pedagogic evaluations in Part B involve neutron spectra, angular distributions, and the dose impact of facility characteristics. With the SP 4” insert removed and the Lead-Boron (44”) Bucket (LB–44) in the reactor cavity, Total Effective Dose (TED) within the CC beamline is ≈140 rem per 300 MJ of reactor yield (or 3900 rem per hour at 100% Steady-State (SS) power). With no SP (unshielded) and a Free-Field (FF) cavity, TED within the beamline is ≈610 rem per 300 MJ (or 17000 rem per hour at 100% SS power). Due to the predicted collimation of radiation by the reactor pool (and partial SP, if present), beamline dose is much greater than the scattered radiation field surrounding the cavity and reactor tank. Comparisons are made to beamline dosimetry measurements to validate the model. Model predictions agree reasonably well (⪅10%) with measured quantities of neutron fluence, gamma fluence, and spectral metrics. Away from the beamline, comparisons made to previous dose measurements in the HB agreement within an order of magnitude.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2026

ACRRF High-Bay Dose Calculations using MCNP (Part B)

ACRR radiation outputs through vertical cavities have been documented in two reports. In Part B, the maximum dose from the unshielded central cavity, FREC-II, and NRS is calculated to inform the safety basis. The maximum dose is ≈1430 mrem per 300 MJ, or ≈40,930 rem/hr for full-power operation. A verification study completes the V&V of the modeling. Supplementary studies of variance-reduction techniques, model sensitivities, and aircraft dose above the ACRRF are included.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2025

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Development of MCNP Training Modules for Safeguards Practitioners [Abstract]

The Monte-Carlo N-Particle (MCNP) software developed at LANL is the most widely used neutron transport code in the world. It is an essential tool for a variety of applications including detector development and design, nuclear fuel burnup simulation, criticality safety, and nondestructive assay system optimization. For this reason, it is indispensable within the safeguards and materials control & accountability (MC&A) communities. Multiple MCNP training courses have been created and taught over the last several decades by the MCNP development team at LANL, however there are no existing courses that cover specialized topics considered fundamental to NDA and safeguards models. To fill this gap, the MCNP team and Safeguards Science and Technology group at LANL have co-created a set of training modules customized to meet the specialized needs of the safeguards and MC&A communities. The basic modules cover concepts such as NDA system optimization, He-specific and other capture tallies, and tools for improved theoretical understanding. An advanced module was also created to cover topics including variance reduction for active interrogation simulations, use of the LANL MCNPTools post-processor, PTRAC (particle tracking) and list-mode data simulations, and fuel burnup simulations. The training modules teach to the latest and most state-of-the-art MCNP features and tools released by the development team at LANL and are intended to be taught jointly by the developers and safeguards experts. Ultimately, we hope that creation of these modules will serve to capture and convey the safeguards modeling and MCNP expertise at LANL, and that we will be able to share the modules more broadly with the MC&A and safeguards communities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2022

Accelerated statistical failure analysis of multifidelity TRISO fuel models

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗