Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematics and computing”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging public AI tools to explore systems biology resources in mathematical modeling

Predictive mathematical modeling is an essential part of systems biology and is interconnected with information management. Systems biology information is often stored in specialized formats to facilitate data storage and analysis. These formats are not designed for easy human readability and thus require specialized software to visualize and interpret results. Therefore, comprehending modeling and underlying networks and pathways is contingent on mastering systems biology tools, which is particularly challenging for users with no or little background in data science or system biology. To address this challenge, we investigated the usage of public Artificial Intelligence (AI) tools in exploring systems biology resources in mathematical modeling. We tested public AI’s understanding of mathematics in models, related systems biology data, and the complexity of model structures. Our approach can enhance the accessibility of systems biology for non-system biologists and help them understand systems biology without a deep learning curve.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop

The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Mathematical Foundation for Quantum Computing of Electromagnetic Wave Propagation in Dielectric Media

Can quantum computers effectively simulate the propagation and scattering of electromagnetic waves in a classical plasma? This chapter introduces some of the basic concepts in mathematics and physics essential to answering that question. The numerical simulations of Maxwell equations for wave propagation in dielectrics are constrained by technological limitations of the present-day computers. In contrast, there has been ample fanfare around quantum computers and their potential to far exceed the performance of traditional computers. Whether the enhanced capabilities of a quantum computer can be put to use for simulating topics in classical physics is a source of intrigue and curiosity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

2025 Workshop on Envisioning Frontiers in AI and Computing for Biological Research: Position Papers

This workshop aims to identify key research directions for transforming biology using artificial intelligence (AI), machine learning (ML) and computational methods to facilitate the discovery of new behaviors, mechanisms, and designs of biological processes relevant to DOE missions, underpinning a broader U.S. bioeconomy. By developing novel AI/ML technologies to analyze and interpret complex biological data, researchers can organize and simulate biological processes at various scales as well as advance predictive understanding and manipulation of biological systems. This integration of computation, experimentation, and next-generation experimental technologies can lead to discoveries in new biological behaviors and mechanisms relevant to DOE missions. The focus is on how advanced computational and mathematical methods can impact this mission by exploring digital twins, foundation models, automated laboratory experiments, modeling of complex living systems, and data-driven approaches for the biodesign of plants and microbial systems. While data management is important, it is not the primary focus of this workshop, which will assess the current state, trends, and AI/ML challenges at the interface between biology and computational science to identify opportunities for high-impact research at their intersection. The goal is to define research needs and opportunities that align with biological sciences, computational sciences, and applied mathematics research.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Brochure on the 2024 ASCR Workshop on Energy-Efficient Computing for Science

Large-scale computing has enabled numerous scientific discoveries, including ground-breaking achievements facilitated by the US Department of Energy (DOE) supercomputers and advances in applied mathematics and computer science. While important advances were made in energy efficiency to enable exascale computing, continued efforts are needed to dramatically improve the energy efficiency of the next generation of high-performance computing (HPC) systems and, more broadly, AI data centers. Without substantial improvements in energy efficiency, the energy consumption associated with computing could become a limiting factor for future scientific discovery, national security, and technological advancement.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Reduced-order modeling for efficient cross section library development in high-temperature gas reactor pebble-bed depletion analysis

Accurate modeling of running-in and equilibrium conditions in pebble-bed reactors (PBRs) requires precise microscopic multigroup neutron cross sections. In Griffin, deterministic neutronics calculations rely on multivariate interpolation over large cross section libraries, resulting in significant memory usage and performance bottlenecks. This work, together with a companion paper on Griffin integration, explores reduced-order models (ROMs) to replace interpolation with lightweight surrogates. Several ROM techniques are benchmarked, with deep neural networks (DNNs) demonstrating superior memory efficiency, scalability, and predictive accuracy. A total of 295 DNNs were trained to build a comprehensive isotope library, integrated into Griffin through a custom LibTorch interface for depletion analysis. Initial results demonstrate that DNN-based ROMs drastically reduce memory demands while preserving accuracy, enabling finer tabulations and additional state variables without overhead. In conclusion, the framework also supports online cross section generation and real-time DNN updates through transfer learning, improving fidelity by capturing self-shielding and evolving nuclide compositions during burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Developing a digital twin framework for remotely monitoring nuclear reactor facilities

A digital twin must seek to represent all applicable functional components of the system of interest. Different expertise is required for understanding the physical system being modeled than the skills needed for transforming those models into a functional digital twin through physics modeling, machine learning analysis, and visualization. The diversity of knowledge requires a multi-disciplinary team to ensure all system details are captured. Team members also need a method to verify that the data they generate within their domain can be effectively communicated to professionals in other fields. To address this challenge, this work provides an approach for developing a digital twin framework to remotely monitoring nuclear facilities. Through this, general knowledge of the framework is presented along with two examples to solidify the process. The AGN-201 digital twin and microreactor digital twins provide varying levels of complexity in a potential nuclear facility, where common threads are identified and lessons learned are provided. The goal of this research is to aid future researchers by providing a formula for a successful digital twin and in turn reducing the development time of nuclear system digital twins, specifically for remote monitoring.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Modeling heat pipe startup and noncondensable gases in Sockeye

For this work, a one-dimensional gas mixture flow model was developed and implemented in the heat pipe code Sockeye to model the effects of noncondensable gases. Additionally, a startup model based on the dusty gas model was implemented to model the transition from rarefied gas dynamics to continuum flow, which occurs during the frozen startup of high-temperature heat pipes. Multiple startup and noncondensable gas models were tested against experimental data for sodium heat pipes, showing excellent agreement. Additionally, the newly developed gas mixture model for modeling noncondensable gas is further tested with a theoretical case study with arbitrary heating configurations. Finally, several recommendations and conclusions are made from the studies in this work to guide future heat pipe modeling efforts.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Assessment of RELAP5-3D Code with Molten Salt Heat Transfer Experiments

The accurate thermal-hydraulic assessment of thermal storage systems is crucial for addressing the integrity and performance of the storage system design. This is particularly important for thermal storage systems using molten salts as a heat transport and storage medium, as the chemical corrosion and erosion by the high-temperature molten salts can cause serious damage to the structural components of the storage system. To understand these effects for TerraPower’s Natrium® Demonstration Reactor design, the system thermal-hydraulic analysis code, RELAP5-3D, is utilized to analyze the thermal storage system. This study evaluates two heat transfer correlations implemented in the RELAP5-3D code—the Dittus-Boelter and Gnielinski correlations—using selected benchmark cases from two molten salt heat transfer experiments conducted at Xi’an Jiao Tong University and the German Aerospace Center. The Nusselt numbers calculated using the Gnielinski correlation agree with the experimental data within ±5% of the relative deviations at 300°C and 400°C. With the increasing Reynolds numbers, the Dittus-Boelter correlation underestimates the Nusselt numbers by up to 22% compared to the Gnielinski correlation. Comparison of the RELAP5-3D calculation results with experimental data at a high temperature of 550°C revealed that the thermo-chemical characteristics of solar salt at high temperatures surpassing the decomposition temperatures of nitrate salts reduce the accuracy of heat transfer model of the RELAP5-3D code. Specifically, it has been observed that the temperatures of the wall surface and liquid near the wall can surpass the decomposition temperatures, even though the bulk temperature of molten salts remains significantly lower than these decomposition temperatures. In summary, this study recommends the use of the Gnielinski correlation for the heat transfer analysis of molten salt, rather than the Dittus-Boelter correlation.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2026

Modeling Flow in a Microreactor Core: From High-Fidelity CFD to Subchannel Analysis

The accurate prediction of pressure drop in tightly packed, low–Reynolds number (Re) bare rod bundles is essential for the thermal-hydraulic design of the Microreactor Applications Research Validation and EvaLuation (MARVEL) reactor and other microreactor concepts. However, existing friction factor correlations, particularly the upgraded Cheng-Todreas (UCTD) correlation, have limited validation for the small pitch-to-diameter ratios (P/Ds) and transitional flow conditions characteristic of these systems. In this work, we perform high-fidelity large-eddy simulations (LESs) of both an infinite bare rod bundle and a finite bare 37-pin scalloped rod bundle across the range 1000≤ 𝑅𝑒 ≤5500. The simulations reveal strong gap vortex–driven transitional behavior and indicate that the UCTD may underpredict the friction factor by up to 28% at 𝑃/𝐷 = 1.05. Using the LES-calculated pressure drops, we formulate a new friction factor correlation that follows the Cheng-Todreas functional form but is calibrated for low-Re and tightly packed geometries representative of a MARVEL-like reactor. The correlation is implemented in the MOOSE (Multiphysics Object-Oriented Simulation Environment) subchannel module and compared against both the LES and UCTD predictions. Across all subchannel types, the proposed model reduces the streamwise velocity differences from as high as 44% (UCTD) to below 9%, and decreases the pressure gradient differences from 13% to 25% (UCTD) to 0.7% to 7% relative to the LES results. These results suggest that the new correlation has the potential to improve the pressure drop and flow field predictions for such geometries, highlighting the importance of high-fidelity simulations in supporting microreactor thermal-hydraulic model development and motivating future pressure drop experiments for compact rod bundles to further validate these findings.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2025

Accelerated Irradiation Testing and Post-Irradiation Characterization: U.S.-Based Capabilities for Advanced Nuclear Systems and Radioisotope Production

Irradiation experiments and post-irradiation examinations, together referred to as irradiation testing (IRT), are prerequisites for nuclear fuel and material qualification for the deployment of new and advanced reactors, as well as radioisotope production, thereby ensuring regulatory compliance. Qualified research and test reactors (RTRs) and testing facilities are essential to enable IRT to verify performance and safety under prototypical reactor conditions. In the past, qualification of new fuels or structural materials required about 20 years. Synergist strategies, advanced tools, and qualified methods are needed to greatly reduce this timeframe of IRT and radioisotope production. This study, termed accelerated-IRT, focuses on identifying gaps and leveraging U.S.-based RTRs and material testing capabilities, leveraging the preliminary evaluation and qualification of selected RTRs to provide a generic as well as specific-case solution paths forward, ensuring adherence to stringent regulatory standards. Furthermore, IRT and radioisotope production utilizing qualified RTRs necessarily includes modeling and simulation to support the design (i.e. neutronics, thermal, and structural aspects) and manufacturing of irradiation test specimens, vehicles, capsules, apparatuses, and flow loops. In addition, IRT can be improved by applying advanced manufacturing techniques and in-pile sensors and instrumentation, as discussed in this study.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Detection of Diversion in a Realistic Heat Pipe Microreactor Using Supervised Machine Learning

Microreactors (MRs) pose new challenges for international safeguards. Here, their small size and mass reproducibility make them ideal for deployment in greater numbers and in remote locations, making the job of safeguards inspectors more challenging. Machine learning (ML) is currently being applied to many fields to augment human performance and increase automation; in particular, ML could be used to provide insight for international inspectors to help detect the diversion of nuclear fuel from MR cores. Four ML model types (k-nearest neighbors, decision tree, random forest, and histogram-based gradient boosted ensemble) were trained on integrated flux and critical control drum angle data generated with Serpent 2 for a realistic heat pipe MR design, achieving nearly 100% binary classification accuracy of nominal and diversion core configurations by the end of 1 full power year for three of the four model types. Regression model variants were also trained, using the same input data, for predicting the number of fuel pins diverted. Root-mean-square errors below 5% of the total number of fuel pins were achieved by the 1 full power year mark for all models.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Integrating Cyber-Informed Engineering into Process Automation

As organizations increasingly automate their core missions and essential functions to address business risks and enhance efficiency, process automation becomes pivotal. This shift, involving minimal or no manual intervention, significantly impacts an organization's cyber-risk landscape. While automation drives efficiencies, it also introduces new cyber risks if not properly managed. Cyber-Informed Engineering (CIE) provides a proactive framework for managing these digital risks, enhancing cyber-resilience in process automation. This document supports organizations in applying CIE principles to mitigate the cyber risks associated with automation. The outlined approach can be independently implemented to improve any organization’s cyber-resilience, ensuring that the advantages of automation do not result in unaddressed or unmanaged digital risks. It serves as a starting point, offering considerations for integrating CIE principles and practices into organizational processes. CIE is presented as an iterative process, fostering continuous improvement and reinforcing the engineering and operational cultures to manage digital risks effectively. The document is structured as follows: Section 1 provides background on CIE and process automation, and their integration. Section 2 explores the twelve CIE principles in the context of process automation, highlighting key questions, engineering considerations, and implications for digital risk management. Section 3 synthesizes the findings and offers recommendations to advance resilience by design.

42 - ENGINEERING↗
DOE OSTI2025

Cyber Conservative Operations

In an era of increasingly sophisticated and pervasive cyber threats, robust cyber resilience strategies are more critical than ever. This paper introduces the concept of Cyber Conservative Operations, a proactive approach designed to assist critical infrastructure owners and operators in managing risk and maintaining resilience in the face of imminent, yet not occurring, cyber events. By leveraging the principles of Cyber-Informed Engineering (CIE) and the energy sector’s practice of conservative operations, Cyber Conservative Operations offer a framework for planning and executing coordinated active defense and resilience-oriented actions ahead of cyber events. This approach aims to minimize the consequences of digitally-enabled hazards and ensure swift recovery from anticipated cyber threats. Cyber Conservative Operations enhance the ability of owners and operators to execute pre-planned defense and resilience actions, thereby reducing the impact of digitally-enabled hazards. These operations are crucial for addressing impacts that cannot be precisely quantified or forecasted and for preparing organizations for rapid recovery from imminent digital threats. The paper begins with a discussion of conservative operations as applied to the bulk power system (BPS), a current mechanism allowing BPS entities to enact defensive operating plans to mitigate impending grid unreliability. Building on this model, we present a concept for implementing cyber conservative operations at asset owner facilities. The paper concludes with two case studies of cyber conservative operations drawn from high-profile cyber events, illustrating the practical application and benefits of this proactive approach.

42 - ENGINEERING↗