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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗
DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Evaluation of Flow Routing on the Unstructured Voronoi Meshes in Earth System Modeling

Flow routing is a fundamental process of Earth System Models' (ESMs) river component. Traditional flow routing models rely on Cartesian rectangular meshes, which exhibit limitations, particularly when coupled with unstructured mesh-based ocean components. They also lack the support for regionally refined models. While previous studies have highlighted the potential benefits of unstructured meshes for flow routing, their widespread application and comprehensive evaluation within ESMs remain limited. This study extends the river component of the Energy Exascale Earth System Model to unstructured Voronoi meshes. We evaluated the model's performance in simulating river discharge and water depth across three watersheds spanning the Arctic, temperate, and tropical regions. The results show that while providing several benefits, unstructured mesh-based flow routing can achieve comparable performance to structured mesh-based routing, and their difference is often less than 10%. Although the unstructured mesh-based method could address several existing limitations, this research also shows that additional improvements in the numerical method are needed to fully exploit the advantages of unstructured mesh for hydrologic and ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. Here, in this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

artificial intelligence↗
DOE OSTI2026

Error quantification and comparison of binary neutron star gravitational waveforms from numerical relativity codes

Future gravitational wave detections of merging binary neutron star systems have the possibility to tightly constrain the equation of state of dense nuclear matter. In order to extract such constraints, gravitational waveform models need to be calibrated to accurate numerical relativity simulations of the late inspiral and merger. In this work, we take an essential step toward classifying the error and potential systematics in current generation numerical relativity simulations of merging binary neutron stars. To this end, we perform a direct comparison of two codes (fil, spec), which differ in many aspects, including the numerical methods and discretizations used and equations solved. We find that despite these different approaches, the codes are—within current numerical resolution bounds—fully consistent, and broadly comparable in cost for a given accuracy level. Our results indicate that the error in the waveforms is primarily dominated by the hydrodynamic evolution, consistent with earlier findings in the literature. Finally, we also discuss current limitations and cost estimates for numerical relativity simulations to reach the accuracies required in the era of next-generation gravitational detectors.

gravitational waves↗
DOE OSTI2025

Quantum stabilization of unexpected ordered phases on the honeycomb lattice

In this work, I discuss and showcase the utility of the method called minimally-augmented spin-wave theory (MAGSWT) as a relatively simple semi-analytical approach to the phase diagrams of quantum magnets. It complements numerical methods by providing physical insight into which states are competitive and by yielding approximate phase boundaries that agree well with much more numerically intensive calculations. This approach enabled me to construct the faithful phase diagrams of two paradigmatic honeycomb-lattice models in the quantum S=1/2 limit, the J 1 –J 3 FM-AF and J 1 –J 2 AF models, for the collinear quantum phases that replace or extend the classical ones. The results are in good qualitative and semi-quantitative agreement with state-of-the-art numerical studies for these models, correctly capturing the emergence of unexpected quantum phases and the suppression of classically favored spiral orders by quantum fluctuations. This study provides a much-needed important guidance to the ongoing theoretical and experimental searches of the unconventional quantum states. This work will be of significant and timely interest to both theorists and experimentalists in the field of quantum magnetism, broadly defined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

The Santa Barbara Binary-disk Code Comparison

We have performed numerical calculations of a binary interacting with a gas disk, using 11 different numerical methods and a standard binary-disk setup. The goal of this study is to determine whether all codes agree on a numerically converged solution and to determine the necessary resolution for convergence and the number of binary orbits that must be computed to reach an agreed-upon relaxed state of the binary-disk system. We find that all codes can agree on a converged solution (depending on the diagnostic being measured). The zone spacing required for most codes to reach a converged measurement of the torques applied to the binary by the disk is roughly 1% of the binary separation in the vicinity of the binary components. For our disk model to reach a relaxed state, codes must be run for at least 200 binary orbits, corresponding to about a viscous time for our parameters, 0.2(a 2 Ω B /v) is the kinematic viscosity. The largest discrepancies between codes resulted from the dimensionality of the setup (3D vs. 2D disks). We find good agreement in the total torque on the binary between codes, although the partition of this torque between the gravitational torque, orbital accretion torque, and spin accretion torque depends sensitively on the sink prescriptions employed. In agreement with previous studies, we find a modest difference in torques and accretion variability between 2D and 3D disk models. We find cavity precession rates to be appreciably faster in 3D than in 2D.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗
DOE OSTI2024

Classical dynamics of the antiferromagnetic Heisenberg spin ladder

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the S = 1/2 ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule. Here, we anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly-coupled dimers, situations that remain challenging for alternative numerical methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Fast calculation of diffraction patterns from an ensemble of aligned molecules

We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. Here, the method can also be applied to the calculation of x-ray diffraction patterns.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Level 2 Milestone: Develop and Incorporate Novel Code Verification of Fundamental Equations in Gemma and Set Up Appropriate Tests

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementations of the electric-, magnetic-, and combinedfield integral equations, are frequently used to solve Maxwell’s equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this report, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches in Gemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Infrasonic directivity of monopole, dipole and bipole ground-surface reflected sources

Infrasound (acoustic waves below 20 Hz) can be used to detect, locate and quantify activity in the atmosphere such as volcanic eruptions and anthropogenic explosions. Attempts to quantify volcanic eruption parameters such as exit velocity, plume height and mass flow rate using infrasound data depend strongly on assumptions of the acoustic source type. Infrasonic sources may produce omnidirectional or directional wavefields, while propagation effects, such as interaction with topography, can induce further wavefield directivity that is measured by field instrumentation. Limited sampling of these wavefields can hinder our ability to infer the underlying source, and thus our understanding of the eruption characteristics. Equivalent sources are often used to represent acoustic source mechanisms and resultant wavefields. In this study, we review equivalent acoustic sources as they pertain to infrasonic scale and wavelengths commonly encountered in very local (⁠<5 km range) geophysical field deployments. We highlight the equivalent infrasonic bipole source that can be induced by ground-reflection of an elevated monopole; we are not aware of any prior infrasound studies that use the bipole source concept. We use analytical and numerical methods to explore source directivity of monopole, dipole and bipole ground-reflected sources at infrasonic frequencies as well as the additional directivity complications introduced by interactions with topography. We illustrate that for typical volcano-infrasound wavelengths, increasing height above the ground as well as increasing source frequency leads to increased wavefield directivity. Numerical modelling using a simple omnidirectional monopole source embedded in topography further illustrates that both horizontal and vertical infrasound directionality can be induced by topography at the distance scales appropriate for local volcano infrasound monitoring. Information summarized in this analytical and numerical exploration of infrasound directivity may be used to help guide future volcano-infrasound field deployments intended to estimate source parameters or quantify wavefield directivity. Analytic solutions for simple whole-space or half-space atmospheres provide useful formulations for planning or initially analysing geophysical field-scale experimental data; however, especially at very local distances from the source (⁠<5 km), 3-D simulations are necessary to account for complex topography commonly encountered in volcano-infrasound applications.

Infrasound↗