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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Molecular NMR shieldings, J -couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations

This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. Here, the paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ~Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Quantifying the basic reproduction number and underestimated fraction of Mpox cases worldwide at the onset of the outbreak

In 2022, there was a global resurgence of mpox, with different clinical-epidemiological features compared with previous outbreaks. Sexual contact was hypothesized as the primary transmission route, and the community of men having sex with men (MSM) was disproportionately affected. Because of the stigma associated with sexually transmitted infections, the real burden of mpox could be masked. We quantified the basic reproduction number (R 0 ) and the underestimated fraction of mpox cases in 16 countries, from the onset of the outbreak until early September 2022, using Bayesian inference and a compartmentalized, risk-structured (high-/low-risk populations) and two-route (sexual/non-sexual transmission) mathematical model. Machine learning (ML) was harnessed to identify underestimation determinants. Estimated R 0 ranged between 1.37 (Canada) and 3.68 (Germany). The underestimation rates for the high- and low-risk populations varied between 25–93% and 65–85%, respectively. The estimated total number of mpox cases, relative to the reported cases, is highest in Colombia (3.60) and lowest in Canada (1.08). In the ML analysis, two clusters of countries could be identified, differing in terms of attitudes towards the 2SLGBTQIAP+ community and the importance of religion. Given the substantial mpox underestimation, surveillance should be enhanced, and country-specific campaigns against the stigmatization of MSM should be organized, leveraging community-based interventions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Transforming Energy Through Computational Excellence: A View From NREL

At the National Renewable Energy Laboratory (NREL)—a U.S. Department of Energy laboratory—computational science, high-performance computing, applied mathematics, advanced computer science, visualization, and data play a pivotal role in advancing energy abundance, affordability, security, and reliability. From fundamental scientifc discovery to systems engineering and analysis, NREL researchers tackle market-relevant challenges to develop solutions for an independent energy system that is reliable, resilient and secure. Collaborative partnerships with industry, government, and academia ensure that our research remains cutting edge, impactful, applicable, and aligned with real-world energy needs. This special issue of Computing in Science & Engineering highlights exemplary NREL projects where computational tools and methodologies drive discovery and accelerate innovation in scalable and integrated energy systems. The featured articles explore the role of computational modeling, high-performance computing, generative AI, and adaptive computing in advancing independent energy solutions, optimizing sustainability research, and enhancing decision-making for energy solutions using a broad mix of energy technologies. Here, these contributions demonstrate how NREL’s computational research bridges the gap between theoretical advancements and practical implementation, emphasizing interdisciplinary collaboration and a commitment to innovation, with a focus on translating computational excellence into real-world impact, thus accelerate progress toward national energy goals. By showcasing cutting-edge research at the intersection of computational science and energy systems, this issue aims to inspire and inform researchers, practitioners, and policymakers dedicated to shaping a more reliable energy future.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Hierarchical Optimization Method for Electric Vertical Takeoff and Landing Aircraft Network Design

Electric vertical takeoff and landing aircraft (eVTOLs) are expected to serve urban air mobility in a station-to-station configuration, which makes the optimal network design of eVTOL stations a critical question to explore. Existing approaches often face limitations, such as the inability to interact station locations with demand or difficulty in finding the optimal solution for large study regions. Here, this paper first proposes a mathematical model to generate optimal eVTOL station locations while considering associated potential eVTOL demand, and then proposes a heuristic algorithm, Hierarchical Optimization MEthod (HOME), to efficiently solve the model. With a case study of Southern California, HOME was compared to 1) directly solving the original integer linear programming-based network design problem, and 2) employing the widely used genetic algorithm. Results suggest that HOME can find optimal solutions with limited computational resources. The proposed framework powered by HOME provides a computationally efficient way to support urban air mobility planning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A modern concept of Lagrangian hydrodynamics

Here, we offer a modern interpretation of Lagrangian hydrodynamics as employed in Lagrangian simulations of compressible fluid flow. Our main result is to show that artificial viscosity, traditionally viewed as a numerical artifice to control unphysical oscillations in flows with shocks, actually represents a physical process and is necessary to derive accurate simulations in any compressible flow. We begin by reviewing the origins of two numerical devices, artificial viscosity and finite-volume methods. We proceed to construct a mathematical (PDE) model that incorporates those numerics and in which a new length scale, the observer, arises representing the discretization. Associated with that length scale, there are new inviscid fluxes that are the artificial viscosity as first formulated by Richtmyer and an artificial heat flux postulated by Noh but typically not included in Lagrangian codes. We discuss the connection of our results to bivelocity hydrodynamics. We conclude with some speculation as to the direction of future developments in multidimensional Lagrangian codes as computers get faster and have larger memories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Solution Method for the Filtered Lifting Line Theory

The filtered lifting line theory presents a continuous form of the inviscid momentum equations of flow over a lifting device, such as a wing or rotor blade, using body forces without mathematical singularities. This theory is also consistent with an actuator line representation of a lifting device. In this work, we present a reformulation of the equations in terms of the local flow angle along the line, which allows solving the stand-alone equations using multivariate root-finding algorithms. This approach can be used to obtain a fast, computationally inexpensive solution of the loading distribution along a wing without the need to perform computational fluid dynamic simulations. We study the requirements in terms of resolution in the spanwise direction and establish the criteria for spacing and minimum amount of points required along the blade to obtain converged solutions. The solutions are compared to results from large-eddy simulations, and we observed excellent agreement with less than a percent difference in quantities along the blade between the methods.

17 WIND ENERGY↗
DOE OSTI2025

Modeling suggests SARS-CoV-2 rebound after nirmatrelvir-ritonavir treatment is driven by target cell preservation coupled with incomplete viral clearance

In a subset of SARS-CoV-2-infected individuals treated with the antiviral nirmatrelvir-ritonavir, the virus rebounds following treatment. The mechanisms driving this rebound are not well understood. We used a mathematical model to describe the longitudinal viral load dynamics of 51 individuals treated with nirmatrelvir-ritonavir, 20 of whom rebounded. Target cell preservation, either by a robust innate immune response or initiation of N-R near the time of symptom onset, coupled with incomplete viral clearance, appears to be the main factor leading to viral rebound. Moreover, the occurrence of viral rebound is likely influenced by the time of treatment initiation relative to the progression of the infection, with earlier treatments leading to a higher chance of rebound. A comparison with an untreated cohort suggests that early treatments with nirmatrelvir-ritonavir may be associated with a delay in the onset of an adaptive immune response. Nevertheless, our model demonstrates that extending the course of nirmatrelvir-ritonavir treatment to a 10-day regimen may greatly diminish the chance of rebound in people with mild-to-moderate COVID-19 and who are at high risk of progression to severe disease. Altogether, our results suggest that in some individuals, a standard 5-day course of nirmatrelvir-ritonavir starting around the time of symptom onset may not completely eliminate the virus. Thus, after treatment ends, the virus can rebound if an effective adaptive immune response has not fully developed. These findings on the role of target cell preservation and incomplete viral clearance also offer a possible explanation for viral rebounds following other antiviral treatments for SARS-CoV-2.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Targeted Adaptive Design

Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. Here, we abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated expected log-predictive probability density of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Towards Seamless Interoperability of MPI-OpenMP Applications

A chasm exists between mathematical software libraries written for MPI-based applications and those written for OpenMP applications. Recently, however, PETSc enables the simple use of its MPI-based linear solvers from OpenMP applications. Separately, the MPICH MPI development team has started a new project to allow almost seamless MPI use in OpenMP applications. Both proposed approaches would result in a similar user experience. Here, we discuss the reasons for these projects and their potential for providing more numerical library choices for OpenMP applications, including the unlimited assortment of linear solvers available in PETSc. In addition, we present the performance of an application using the first approach, demonstrating its efficacy.

MPI↗
DOE OSTI2024

Extracting and Interpreting Electrochemical Impedance Spectra (EIS) from Physics-Based Models of Lithium-Ion Batteries

This paper implements a highly efficient algorithm to extract electrochemical impedance spectra (EIS) from physics-based battery models (e.g., a P2D model). The mathematical approach is different from how EIS is practiced experimentally. Experimentally, the voltage (current) is harmonically perturbed over a wide range of frequencies and the amplitude and phase shift of the corresponding current (voltage) is measured. The experimental approach can be implemented in simulation software, but is computationally expensive. The approach here is to determine locally linear state-space models from the full physical model. The four Jacobian matrices that are the basis of the state-space models can be derived by numerical differentiation of the physical model. The EIS is then extracted from the state-space model using computationally efficient matrix-manipulation techniques. The algorithm can evaluate the full EIS at an instant in time during a transient, independent of whether the battery is in a stationary state. The approach is also able to separate the full-cell impedance to evaluate partial EIS, such as for a battery anode alone. Although such partial EIS is difficult to measure experimentally, the partial EIS provides valuable insights in interpreting the full-cell EIS.

25 ENERGY STORAGE↗
DOE OSTI2024

Analyzing School Bus Electrification in Richmond, Virginia

School buses are an essential component of the transportation infrastructure, serving as a lifeline for students across the globe. However, the widespread use of diesel school buses has raised concerns about the health impact on millions of students exposed to harmful emissions daily. Recognizing this issue, school districts worldwide are urgently seeking cleaner energy alternatives. Electric school buses emerge as an environmentally friendly and sustainable option, fostering a healthier environment for both students and communities. However, school bus electrification faces the challenges of high upfront cost, cumbersome charging management, and constraints from power grids. To help school bus operators address those challenges, this study presents a data-driven analysis for school bus electrification. This study considered a real-world school bus system in Richmond, VA, and developed a mathematical programming model to analyze the system design, charging strategies, and charging load profiles for the electrification scenario. The study evaluated different charging strategies based on model outcomes, aiming to optimize efficiency and effectiveness. Ultimately, this research generated electric school bus charging demand profiles under various scenarios, shedding light on the feasibility and implications of transitioning to electric-powered school buses.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

ECP libraries and tools: An overview

The Exascale Computing Project (ECP) Software Technology and Co-Design teams addressed the growing complexities in high-performance computing (HPC) by developing scalable software libraries and tools that leverage exascale system capabilities. As we enter the exascale era, the need for reusable, optimized software solutions that can handle the unique challenges posed by these systems becomes increasingly important. The primary challenges the ECP teams faced were to create software libraries and tools that are performant on exascale architectures and portable and usable across diverse hardware platforms. Efforts addressed issues related to concurrent execution, memory management, and the integration of heterogeneous computing resources, such as GPUs from multiple vendors. The ECP’s strategy involved a structured development process encompassing the creation, optimization, and deployment of software in collaboration with industry, academia, and national laboratories. The project was organized into several technical areas: co-design of domain-specific suites with target applications, programming models and runtimes, development tools, mathematical libraries, data and visualization tools, and software ecosystem and delivery mechanisms. ECP has successfully developed a large portfolio of software libraries and tools that demonstrate significant improvements in performance and scalability on exascale systems. These products have been integrated into the Department of Energy’s computing facilities, supporting various scientific applications and ensuring robust performance across different hardware setups. ECP advancements in software development for exascale computing highlight the importance of a collaborative and adaptive approach to handling next-generation HPC systems complexities. The lessons learned emphasize the need for continuous engagement with end-users and vendors, and the importance of maintaining a balance between innovation and practical implementation. Future efforts will focus on ensuring scalability, keeping pace with rapid hardware advancements, and further enhancing the interoperability and usability of the software ecosystem. In conclusion, subsequent articles in this special issue provide in-depth discussions and case studies into specific library and tool efforts.

97 MATHEMATICS AND COMPUTING↗