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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Using PCA and PLS on publicly available data to predict the extractability of hydrocarbons from shales

Prediction of hydrocarbon extraction from shale requires specialized knowledge of shale play characteristics and analysis to assess effective, economical, and sustainable implementation of oil and natural gas production. In this paper, we present a statistical approach that can be used as a preliminary investigation into the hydrocarbon resource potential of a shale play based on limited data. Statistical algorithms for Principal Component Analysis (PCA) and Partial Least Squares Regression (PLS) were used to determine if depositional environments and lithographic boundary characteristics of different plays allowed prediction of specific production parameters. This project characterizes Eagle Ford and Utica formations—two high-producing shale plays in the United States—and Banff/Exshaw and Colorado formations—two recently assessed shale plays in Alberta, Canada. Partial Least Squares Regression models were unable to model gas production parameters from predictor variables, highlighting the complexity of gas formations and the need for data on microscale petrophysical characteristics. In contrast, oil production parameters were better predicted, because bulk variables such as mineral composition appeared to correlate with oil location in mineral interfaces. As expected, a PLS model's predictive capabilities increased with specificity of data sets to particular regions of a shale play. Finally, this study indicates how PCA and PLS modeling could assist stakeholders to make preliminary decisions regarding hydrocarbon extraction, especially when limited to publicly available petrophysical data.

03 NATURAL GAS↗
DOE OSTI2018

In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi

Lignocellulose is an abundant and renewable resource that holds great promise for sustainable bioprocessing. However, unpretreated lignocellulose is recalcitrant to direct utilization by most microbes. Current methods to overcome this barrier include expensive pretreatment steps to liberate cellulose and hemicellulose from lignin. Anaerobic gut fungi possess complex cellulolytic machinery specifically evolved to decompose crude lignocellulose, but they are not yet genetically tractable and have not been employed in industrial bioprocesses. Here, we aim to exploit the biomass-degrading abilities of anaerobic fungi by pairing them with another organism that can convert the fermentable sugars generated from hydrolysis into bioproducts. By combining experiments measuring the amount of excess fermentable sugars released by the fungal enzymes acting on crude lignocellulose, and a novel dynamic flux balance analysis algorithm, we screened potential consortia partners by qualitative suitability. Microbial growth simulations reveal that the fungus Anaeromyces robustus is most suited to pair with either the bacterium Clostridia ljungdahlii or the methanogen Methanosarcina barkeri—both organisms also found in the rumen microbiome. By capitalizing on simulations to screen six alternative organisms, valuable experimental time is saved towards identifying stable consortium members. This approach is also readily generalizable to larger systems and allows one to rationally select partner microbes for formation of stable consortia with non-model microbes like anaerobic fungi.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗
DOE OSTI2018

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Abstract Subsurface flow model calibration involves many more unknowns than measurements, leading to ill‐posed problems with nonunique solutions. To alleviate nonuniqueness, the problem is regularized by constraining the solution space using prior knowledge. In certain sedimentary environments, such as fluvial systems, the contrast in hydraulic properties of different facies types tends to dominate the flow and transport behavior, making the effect of within facies heterogeneity less significant. Hence, flow model calibration in those formations reduces to delineating the spatial structure and connectivity of different lithofacies types and their boundaries. A major difficulty in calibrating such models is honoring the discrete, or piecewise constant, nature of facies distribution. The problem becomes more challenging when complex spatial connectivity patterns with higher‐order statistics are involved. This paper introduces a novel formulation for calibration of complex geologic facies by imposing appropriate constraints to recover plausible solutions that honor the spatial connectivity and discreteness of facies models. To incorporate prior connectivity patterns, plausible geologic features are learned from available training models. This is achieved by learning spatial patterns from training data, e.g., ‐SVD sparse learning or the traditional Principal Component Analysis. Discrete regularization is introduced as a penalty functions to impose solution discreteness while minimizing the mismatch between observed and predicted data. An efficient gradient‐based alternating directions algorithm is combined with variable splitting to minimize the resulting regularized nonlinear least squares objective function. Numerical results show that imposing learned facies connectivity and discreteness as regularization functions leads to geologically consistent solutions that improve facies calibration quality.

Khaninezhad, Mohammad‐Reza↗
DOE OSTI2018

Generation and application of multivariate polynomial quadrature rules

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Poisson-response Tensor-on-Tensor Regression and Applications

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed of counts are common data in fields such as inter national relations, social networks, epidemiology, and medical imaging, where events occur across multiple dimensions like time, location, and dyads. PToTR accommodates such tensor responses alongside tensor covariates, providing a versatile tool for multi dimensional data analysis. We propose algorithms for maximum likelihood estimation under a canonical polyadic (CP) structure on the regression coefficient tensor that satisfy the positivity of Poisson parameters and then provide an initial theoretical error analysis for PToTR estimators. We also demonstrate the utility of PToTR through three concrete applications: longitudinal data analysis of the Integrated Crisis Early Warning System database, positron emission tomography (PET) image reconstruction, and change-point detection of communication patterns in longitudinal dyadic data. These applications highlight the versatility of PToTR in addressing complex, structured count data across various domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine learning models for rat multigeneration reproductive toxicity prediction

Reproductive toxicity is one of the prominent endpoints in the risk assessment of environmental and industrial chemicals. Due to the complexity of the reproductive system, traditional reproductive toxicity testing in animals, especially guideline multigeneration reproductive toxicity studies, take a long time and are expensive. Therefore, machine learning, as a promising alternative approach, should be considered when evaluating the reproductive toxicity of chemicals. We curated rat multigeneration reproductive toxicity testing data of 275 chemicals from ToxRefDB (Toxicity Reference Database) and developed predictive models using seven machine learning algorithms (decision tree, decision forest, random forest, k-nearest neighbors, support vector machine, linear discriminant analysis, and logistic regression). A consensus model was built based on the seven individual models. An external validation set was curated from the COSMOS database and the literature. The performances of individual and consensus models were evaluated using 500 iterations of 5-fold cross-validations and the external validation data set. The balanced accuracy of the models ranged from 58% to 65% in the 5-fold cross-validations and 45%–61% in the external validations. Prediction confidence analysis was conducted to provide additional information for more appropriate applications of the developed models. The impact of our findings is in increasing confidence in machine learning models. We demonstrate the importance of using consensus models for harnessing the benefits of multiple machine learning models (i.e., using redundant systems to check validity of outcomes). While we continue to build upon the models to better characterize weak toxicants, there is current utility in saving resources by being able to screen out strong reproductive toxicants before investing in vivo testing. The modeling approach (machine learning models) is offered for assessing the rat multigeneration reproductive toxicity of chemicals. Our results suggest that machine learning may be a promising alternative approach to evaluate the potential reproductive toxicity of chemicals.

consensus model↗
DOE OSTI2021

VERIFICATION OF TRISO FUEL BURNUP USING MACHINE LEARNING ALGORITHMS

Pebble Bed Reactors are fueled with fuel pebbles that are circulated multiple times through the reactor vessel before discharge. During the normal operation of a PBR, ejected pebbles are returned to the reactor or discharged depending on the fuel burnup and physical condition of the pebbles. The burnup measurement is usually based on detected radiation signatures of fission products accumulated in the pebble fuel over burnup. Previous research has shown that height of photopeaks of fission products, such as 134Cs, 137Cs, 154Eu, etc., can be used independently or in combination to infer or predict the level of burnup in the fuel. However, it remains challenging to measure such complex sources due to self-shielding effects, strong radiation background and intervening materials. Another operational challenge is the required high throughput of burnup measurement, which necessitates limited measurement time and thus impacts quality of measured gamma-ray spectra. Hence, advanced spectral analysis methods are needed to analyze the noisy gamma spectra and predict the burnup values. We propose to use machine learning (ML) method to interpret gamma-ray spectra and predict the burnup values of the pebbles. ML has achieved widespread success and adoption across a few domains that require pattern recognition and analysis in varied data types. In this work, we apply three proven ML approaches - multilayer perceptrons, convolutional neural networks, and transformers - to the task of predicting fuel burnup from measured gamma spectra, and compile a dataset of simulated spectra for training and validation of the ML models. In this paper, we will discuss the network architecture of these three ML approaches and compare the performance of the simplest of these (MLP) to a standard linear regression.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2023

Advanced Fuel Cycle Cost Basis Report: Module D1-7 Contact-Handled Pelletized Pressurized Heavy Water (PHWR) UOX Fuel Fabrication (Rev.1)

In addition to literature-based pressurized heavy-water reactor (PHWR) fuel price information in the 2017 AFC-CBR, the what-it-takes (WIT) unit cost data in this update is informed by new analysis and escalation of the 1978 PHWR-UOX fuel life cycle cost (LCC) data from ORNL reports prepared for the 1977–1980 Nonproliferation Alternative Systems Assessment Program (NASAP). (These reports are referenced and summarized in detail in Module D1-PR.) The PHWR fuel fabrication LCC data in these reports is scaled from a bottom-up cost estimate for a reference technology pressurized-water reactor (PWR)—uranium oxide (UOX) fuel fabrication plant by using algorithms that consider the manufacturing process complexity, fuel design complexity, plant floor space requirements, and the radiation and health, safety, and environmental (HS&E) regulatory environment of PHWR-UOX fuel production vis-à-vis light-water reactor (LWR)-UOX production (PWR fuel in this case). The module name has been changed from “Canadian Deuterium Uranium (CANDU)” to the more generic PHWR fuel fabrication in recognition that not all power reactors that might use this fuel type are considered. Unfortunately, the detailed algorithms and their design bases were not archived at the end of the NASAP effort of the commercial CANDU concept specifically developed in the middle of the last century by Atomic Energy of Canada Limited (AECL).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Verification of Triso Fuel Burnup Using Machine Learning Algorithms

Pebble Bed Reactors are fueled with fuel pebbles that are circulated multiple times through the reactor vessel before discharge. During the normal operation of a PBR, ejected pebbles are returned to the reactor or discharged depending on the fuel burnup and physical condition of the pebbles. The burnup measurement is usually based on detected radiation signatures of fission products accumulated in the pebble fuel over burnup. Previous research has shown that height of photopeaks of fission products, such as 134 Cs, 137 Cs, 154 Eu, etc., can be used independently or in combination to infer or predict the level of burnup in the fuel. However, it remains challenging to measure such complex sources due to self-shielding effects, strong radiation background and intervening materials. Another operational challenge is the required high throughput of burnup measurement, which necessitates limited measurement time and thus impacts quality of measured gamma-ray spectra. Hence, advanced spectral analysis methods are needed to analyze the noisy gamma spectra and predict the burnup values. We propose to use machine learning (ML) method to interpret gamma-ray spectra and predict the burnup values of the pebbles. ML has achieved widespread success and adoption across a few domains that require pattern recognition and analysis in varied data types. In this work, we apply three proven ML approaches - multilayer perceptrons, convolutional neural networks, and transformers - to the task of predicting fuel burnup from measured gamma spectra, and compile a dataset of simulated spectra for training and validation of the ML models. In this paper, we will discuss the network architecture of these three ML approaches and compare the performance of the simplest of these (MLP) to a standard linear regression.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative data sets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student t process regression. We apply Student t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via colouring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics and classic machine learning clustering algorithms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Generation and application of multivariate polynomial quadrature rules

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second main contribution comes in the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

FORCE Update 2024

The Framework for Optimization of Resources and Economics (FORCE) tool suite is the U.S. Department of Energy’s Nuclear Integrated Energy Systems (IES) Program flagship tool suite for technoeconomic IES analysis of IES. This tool suite is useful for analysis designed to evaluate and improve the technoeconomics of energy production systems, particularly for systems including nuclear technology. In this report, we document the development activity for the FORCE tool suite to extend its capabilities as performed during fiscal year 2024. In addition to reliability and accessibility, capability is one of the three standards guiding the development of the FORCE tool suite and the software codes that are its constituent parts. Extending the capabilities of the FORCE tool suite allows analysis both within the IES program as well as industry, university, and laboratory partners to perform analysis with more accuracy, insight, and impactful narrative. Four areas of capability development were the focus of activity this year: economic parameter uncertainty quantification, multiresolution analysis, components-to-optimization workflow automation, and statespace construction workflows for real-time optimal control. In economic parameter uncertainty quantification, the ability of HERON to capture risk due to scenarios (weather and energy demand uncertainty) was expanded to also include uncertainties in financial parameters such as capital cost or operation and maintenance costs. By including these sources of uncertainty, which are sometimes very large compared with scenario uncertainty, HERON is better able to capture the risk posed by investment in various IES technology. Because of this, analysts can also consider the reduction in risks that can be realized by choice of some technologies. In multiresolution analysis, development activity extended on work completed previously. In fiscal year 2023, methods for decomposing time series signals, such as demand, solar and wind availability, and price profiles, were analyzed and down-selected to those most effective at splitting signals into different resolutions. These resolutions allow considering the influence of different energy demand and supply behaviors across different time scales. For example, energy demand might be divided into seasonal, weekly, and hourly profiles. In fiscal year 2024, this preliminary work was extended and implemented within the Risk Analysis Virtual Environment (RAVEN) risk and uncertainty analysis platform, which is used throughout the FORCE framework. This development of the “multi-resolution time series analysis” (MR-TSA) module in RAVEN allows training synthetic history generators on complex time series. These synthetic history generators can then be used in HERON for generating scenarios that represent possible market and weather scenarios that can be analyzed on different time scales. We envision completing this work in the future, implementing multiresolution dispatch optimization strategies that can make the most beneficial use of these stratified time histories. In components-to-optimization workflow development, workflows for translating user inputs of components into algorithms for algebraic optimization were selected and implemented. Similar algorithms within the Holistic Energy Resource Optimization Network (HERON) were separated from the main code base of HERON and gathered with the components-to-optimization workflows in the new Dispatch Optimization Variable Engine (DOVE) software library. This modularization allows FORCE users to analyze dispatch optimization and energy system duty cycles independently of HERON, which previously was a burdensome task. Additionally, these dispatch optimization algorithms, set up in an independent library, can now be used across all software applications within FORCE, especially including the real-time optimal control software Optimization of Real-time Capacity Allocation (ORCA). Allowing FORCE software to share dispatch optimization algorithms within a single library allows for improved software maintenance and reliability. In statespace characterization workflow development, alternative workflows for optimizing dispatch with additional technical accuracy was the focus, particularly to improve the real-time optimization decision making in ORCA. Using algorithms and workflows initially developed for the Feasible Actuator Range Modifier (FARM), workflows for determining the statespace representation of IES were identified and demonstrated. The resulting dispatch optimization required a more robust optimization algorithm than that originally used in HERON (and moved to DOVE), which required adding an alternate workflow to DOVE that can more accurately match the behavior of physical systems using a partial differential equation representation. In conclusion, capability developments in the FORCE tool suite in fiscal year 2024 have improved the ability of the FORCE tool suite to perform

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Three-Dimensional Grid Visualization for Planning Activities: A Dubai Case Study

National Laboratory of the Rockies (NLR), in collaboration with the Dubai Electricity and Water Authority (DEWA) and Infra-X, has undertaken the Energy Visualization Analysis Project. The aim of this project is to enhance analytical and 3D visualization capabilities for distribution network planning and renewable energy integration. As modern grid continues to evolve with large-scale solar PV deployment and emerging distributed energy resources (DERs), the ability to effectively analyze, visualize, and communicate complex grid behaviors has become increasingly critical. The project focuses on developing empirical use cases based on real distribution feeder data and engineering workflows, ensuring the outcomes are directly aligned with operational environment. Through time-series power flow simulations and nodal hosting capacity analysis, the study quantifies the impacts of high PV penetration on voltage and thermal limits within representative 11 kV feeders. These analyses identify specific nodes and conditions where DER integration challenges arise. Furthermore, a Battery Energy Storage System (BESS) optimization algorithm was applied to determine the optimal size and placement of storage systems that can mitigate network constraints and enhance hosting capacity. The comparative results between base-case and BESS-augmented scenarios clearly demonstrate improvements in network stability and load management efficiency. In parallel, the NLR team developed an immersive 3D visualization framework, enabling interactive exploration of grid simulations using commodity head-mounted display (HMD) systems. This framework transforms conventional 2D simulation data into spatially intuitive visual environments - allowing engineers to analyze feeder conditions, PV hosting potential, and BESS effects in real time. This report represents the first foundational phase in establishing a visualization-driven analytical ecosystem. It provides a methodological foundation for data integration, visualization architecture, and simulation-based decision support, paving the way for large-scale adoption of immersive visualization across DEWA's Smart Grid Initiative, R&D activities, and future network resilience studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative datasets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student-t process regression. We apply Student-t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via coloring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics, and classic machine learning clustering algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Computing material volume fractions on a superimposed mesh as applied to Monte Carlo particle transport simulations

Here, we present a newly implemented ray tracing algorithm in OpenMC for efficiently computing material volume fractions on superimposed meshes in complex geometries. By firing rays along each coordinate direction through the geometry, the approach accumulates track-length data in each mesh element, thereby determining the fractional composition of each material. Scaling studies on three different models—a random tetrahedra configuration, the Frascati Neutron Generator ITER dose rate benchmark, and a stellarator design—show excellent parallel performance, with nearly linear speedup on modern multi-threaded and distributed-memory systems. An analysis of the residual error relative to high-resolution reference solutions demonstrated that under optimal conditions it decreases as 1/R, where R is the number of rays fired, making it straightforward to achieve user-prescribed accuracy. This new functionality enables practical, mesh-based approaches for detailed nuclear analyses in production Monte Carlo workflows without resorting to expensive, fully conformal or unstructured meshing.

Monte Carlo↗
DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗