Search NASA⌕ Search

SEARCH · Search NASA

Results for “functional approximation”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

HfTi_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-titanium (Hf-Ti). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Ti. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on Air Force HPC11 cluster using the VASP 6.5.1. Additional methodology and file structure information is available in the dataset README.txt file.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems

Accurate and quick identification of high-impedance faults (HIFs) is critical for the reliable operation of distribution systems. Unlike other faults in power grids, HIFs are very difficult to detect by conventional overcurrent relays due to the low fault current. Although HIFs can be affected by various factors, the voltage-current characteristics can substantially imply how the system responds to the disturbance and thus provides opportunities to effectively localize HIFs. In this work, we propose a data-driven approach for the identification of HIF events. To tackle the nonlinearity of the voltage-current trajectory, first, we formulate optimization problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations. Numerical studies on the IEEE 123-node test feeder demonstrate the validity and accuracy of the proposed approach for real-time HIF identification.

explainable artificial intelligence↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems: Preprint

Accurate and quick identification of high-impedance faults (HIFs) is critical for the reliable operation of distribution systems. Unlike other faults in power grids, HIFs are very difficult to detect by conventional overcurrent relays due to the low fault current. Although HIFs can be affected by various factors, the voltage-current characteristics can substantially imply how the system responds to the disturbance and thus provides opportunities to effectively localize HIFs. In this work, we propose a data-driven approach for the identification of HIF events. To tackle the nonlinearity of the voltage-current trajectory, first, we formulate optimization problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations. Numerical studies on the IEEE 123-node test feeder demonstrate the validity and accuracy of the proposed approach for real-time HIF identification.

explainable artificial intelligence↗
DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Thermo-hydraulic steam pipe models for district heating simulations: Simplifications to balance accuracy and simulation speed

Steam piping networks are essential for optimizing performance in industrial processes and district heating systems. However, dynamic models that balance thermo-hydraulic accuracy with computational efficiency remain limited. In response, this paper presents a new discretized steam pipe model based on the plug flow approach, capturing key thermo-hydraulic behaviors while simplifying steam phase change processes. Implemented in Modelica, the model accurately calculates temperature and pressure distributions along steam pipelines. To improve computational efficiency for district-scale simulations, five model simplifications are introduced: lumped thermo-hydraulic functions, empirical correlations, fluid state approximations, steady-state dynamics and inclusion of flow derivatives. These simplified models achieve 85%-98% accuracy in predicting pressure drop and condensation losses, including dynamic condensate behavior during pipe warm-up—a factor often overlooked in existing models. The models support diverse network configurations, scaling effectively to systems with multiple distribution pipes and connected building loads. Discrete models provide detailed insights but exhibit a cubic increase in simulation time as the network scales by N connected building O(N 2.42 ). In contrast, lumped models simulate 10–28 times faster than discrete, offering quadratic scaling of simulation time O(N 1.73 ). However, they still require 6 times more computation time than a lossless network, highlighting the inherent computational challenges of modeling compressible fluid flow. In conclusion, the steady-state lumped variant, with its near-linear scalability in computational time O(N 1.01 ), emerges as an efficient solution for preliminary design evaluations and extensive parametric studies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

DONKEY: A Flexible and Accurate Algorithm for Clustering

We propose an accurate clustering algorithm suitable for the varied and multidimensional data sets that correspond to temporal snapshots from on-the-fly nonadiabatic trajectory-based simulations of photoexcited dynamics. The algorithm approximates the underlying probability density function using variable kernel density estimation, with local maxima corresponding to cluster centers. Each data point is then assigned to one of the maxima by employing a maximization procedure. Finally, clusters artificially separated by minor fluctuations in the probability density are merged. The algorithm does not require parameter tuning, which ensures flexibility and reduces the risk of bias. It is tested on several synthetic data sets, where it consistently outperforms conventional clustering algorithms. As a final example, the algorithm is applied to the excited dynamics of the norbornadiene ⇌ quadricyclane (C 7 H 8 ) molecular photoswitch, demonstrating how distinct reaction pathways can be identified.

algorithms↗
DOE OSTI2024

Shock compression of single-crystal austenitic FeCr18Ni12.5 stainless steel to 60 GPa

We measured the austenitic FeCr18Ni12.5 stainless steel Hugoniot as a function of crystallographic direction to approximately 60 GPa. We shock-compressed FeCr18Ni12.5 samples oriented along $\langle$100$\rangle$, $\langle$110$\rangle$, and $\langle$111$\rangle$ to mean stresses ranging 30.5–58.1 GPa via Ta plate impact in a large-bore powder gun and measured the free-surface velocities with laser interferometry. We unambiguously observed the largest post-shock free-surface velocity along $\langle$100$\rangle$ in each experiment, which consequently produced the lowest shock velocity along that orientation. However, the propagation of experimental uncertainties through the impedance matching scheme used to compute the shock velocity produced sufficient uncertainty overlap to preclude definitive conclusion of Hugoniot anisotropy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Effects of artificial collisions, filtering, and nonlocal closure approaches on Hermite-based Vlasov–Poisson simulations

Kinetic simulations of collisionless plasmas are computationally challenging due to phase-space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov–Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard-Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Global fit of electron and neutrino elastic scattering data to determine the strange quark contribution to the vector and axial form factors of the nucleon

We present a global fit of neutral-current elastic (NCE) neutrino-scattering data and parity-violating electron-scattering (PVES) data with the goal of determining the strange quark contribution to the vector and axial form factors of the proton. Previous fits of this form included data from a variety of PVES experiments (PVA4, HAPPEx, G0, SAMPLE) and the NCE neutrino and anti-neutrino data from BNL E734. These fits did not constrain the strangeness contribution to the axial form factor G A s ( Q 2 ) at low Q 2 very well because there was no NCE data for Q 2 < 0.45 GeV 2 . Our new fit includes for the first time MiniBooNE NCE data from both neutrino and antineutrino scattering; this experiment used a hydrocarbon target and so a model of the neutrino interaction with the carbon nucleus was required. Three different nuclear models have been employed: a relativistic Fermi gas model, the superscaling approximation model, and a spectral function model. We find a tremendous improvement in the constraint of G A s ( Q 2 ) at low Q 2 compared to previous work, although more data is needed from NCE measurements that focus on exclusive single-proton final states, for example from MicroBooNE. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Mirror-centered representation of a focusing hyperbolic mirror for X-ray beamlines

Conic sections are commonly used in reflective X-ray optics. Hyperbolic mirrors can focus a converging light source and are frequently paired with elliptical or parabolic mirrors in Wolter type configurations. This paper derives the closed-form expression for a mirror-centered hyperbolic shape, with zero-slope at the origin. Combined with the slope and curvature, such an expression facilitates metrology, manufacturing and mirror-bending calculations. Previous works consider ellipses, parabolas, magnifying hyperbolas or employ lengthy approximations. Here, the exact shape function is given in terms of the mirror incidence angle and the source and image distances.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Laser-driven high-resolution MeV x-ray tomography

The need for high-resolution MeV x-ray tomography to observe the three-dimensional structure of dense, large-sized objects is rapidly increasing for the non-destructive evaluation of critical additively manufactured parts, national security, and other applications. We report a demonstration of high-resolution MeV computed tomography of a dense, large object with a laser-driven x-ray source. A record detector-limited MeV radiograph resolution of < 200 µm as determined with the Bennett approximation of the point spread function was achieved by irradiating millimeter-thick tungsten targets with 300 TW femtosecond laser pulses at a 0.5 Hz repetition rate. A tungsten alloy step wedge spectrometer indicates that the peak of the x-ray emission is between 1 and 2 MeV, with an endpoint energy of 19 MeV. To illustrate the radiographic imaging capability of the system, a tomographic reconstruction of a nickel superalloy turbine blade ( maximum $ρr$ = 139 g/cm 2 ) with sub-millimeter resolution was performed using 2160 individual radiographs. The small x-ray source size opens the prospect of extremely high-resolution tomographs of large, dense objects. This laser-driven approach has major advantages for non-destructive evaluation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Adaptive Methods for Radial Basis Functions

Radial basis functions (RBFs) are a powerful tool for constructing high-order accurate reduced representations of scattered data in arbitrary dimension and on manifolds. We present a method of constructing data approximations in which we utilize a functional tail to capture a global background profile and a RBF neural network (NN) to capture the smaller-scale features. In the RBF NN the RBF centers, matrix shape parameters were selected adaptively for each RBF. We also utilized a geodesic notion of distance on the manifold on which the data lies, e.g., the spherical geodesic for data on the sphere. Although each of these ideas have been been investigated separately in previous works, their combination into a single algorithm is novel. We defined a machine learning problem in which these properties are learned to minimize the data reduction error. We demonstrate the algorithm for applications of scattered data reduction in the plane and on the sphere.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The Vera C. Rubin Observatory Data Preview 1

We present Rubin Data Preview 1 (DP1), the first data from the National Science Foundation–Department of Energy Vera C. Rubin Observatory, comprising raw and calibrated single-epoch images, coadds, difference images, detection catalogs, and ancillary data products. DP1 is based on 1792 optical–near-infrared exposures acquired over 48 distinct nights by the Rubin Commissioning Camera (LSSTComCam) on the Simonyi Survey Telescope at the Summit Facility on Cerro Pachón, Chile in late 2024. DP1 covers ∼15 deg 2 distributed across seven roughly equal-sized noncontiguous fields, each independently observed in six broad photometric bands, ugrizy. The median FWHM of the point-spread function across all bands is approximately 1"14, with the sharpest images reaching about 0." 58. The 5σ point-source depths for coadded images in the deepest field, the Extended Chandra Deep Field South, are u = 24.55, g = 26.18, r = 25.96, i = 25.71, z = 25.07, and y = 23.1. Other fields are no more than 2.2 mag shallower in any band, where they have nonzero coverage. DP1 contains approximately 2.3 million distinct astrophysical objects, of which 1.6 million are extended in at least one band in coadds, and 431 solar system objects, of which 93 are new discoveries. DP1 is approximately 3.5 TB in size and is available to Vera C. Rubin Observatory data rights holders via the Rubin Science Platform, a cloud-based environment for the analysis of petascale astronomical data. While small compared to future LSST releases, its high quality and diversity of data support a broad range of early science investigations ahead of full operations in 2026.

Ground-based astronomy↗
DOE OSTI2025

Computational methods based on density functional theory for reactions and processes involving electronic spin (Final Technical Report)

This award supports one post-doctoral researcher for 1.5 years. Publications that acknowledge this grant: Refs. 1–14. Refs. 3,10,12 assess current methodology for the evaluation of magnetic exchange couplings in transition metal complexes. In particular, Ref. 10 validates the use of an approximate (non-iterative) Green’s function approach for the calculation of magnetic exchange couplings and will be the foundation for Thrust 2 in this proposal. Refs. 3 and 12 focus on widely used density functional approaches based on the standard energy differences methodology for the particular case of oxo-bridged Fe(III) complexes. Refs. 2,4–7,11 apply current methodologies to problems of practical interest in molecular magnetism. Ref. 13 presents a methodology to explicitly simulate the dynamics of open quantum systems within density functional theory (DFT) calculations based on the Liouville-von Neumann equation of motion for quantum systems driven out-of-equilibrium. Ref. 8 uses non-collinear spin DFT to explain the mechanical behavior of magnetic mono-atomic Pt wires produced in break-junction experiments in the presence of a magnetic field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Dynamic Disruption Resilience in Intermodal Transport Networks: Integrating Flow Weighting and Centrality Measures

Resilient intermodal freight networks are vital for sustaining supply chains amid increasing threats from natural hazards and cyberattacks. Transportation resilience has been widely studied; understanding how random and targeted disruptions affect structural connectivity and functional performance remains a key challenge. To address this, this study evaluates the robustness of the US intermodal freight network, which consists of rail and water modes, using a simulation-based framework that integrates graph-theoretic metrics with flow-weighted centrality measures. Disruption scenarios are examined, including random failures as well as targeted node and edge removals based on static and dynamically updated degree and betweenness centrality. To reflect more realistic conditions, flow-weighted degree centralities (WDC) and partial node degradation are considered. Two resilience indicators are used: (1) the size of the giant connected component to measure structural connectivity; and (2) flow-weighted network efficiency (NE) to assess freight mobility under disruption. The results show that progressively degrading nodes ranked by WDC to 60% of their original functionality causes a sharper decline in normalized NE, for up to approximately 45 affected nodes, than complete failure (100% loss of functionality) applied to nodes targeted by weighted betweenness centrality or selected at random. This highlights how partial degradation of high-tonnage hubs can produce disproportionately large functional losses. The findings emphasize the need for resilience strategies that go beyond network topology to incorporate freight flow dynamics.

42 ENGINEERING↗
DOE OSTI2025

Efficient sampling of free energy landscapes with functions in Sobolev spaces

Molecular simulations of biological and physical phenomena generally involve sampling complicated, rough energy landscapes characterized by multiple local minima. In this work, we introduce a new family of methods for advanced sampling that draw inspiration from functional representations used in machine learning and approximation theory. As shown here, such representations are particularly well suited for learning free energies using artificial neural networks. As a system evolves through phase space, the proposed methods gradually build a model for the free energy as a function of one or more collective variables, from both the frequency of visits to distinct states and generalized force estimates corresponding to such states. Implementation of the methods is relatively simple and, more importantly, for the representative examples considered in this work, they provide computational efficiency gains of up to several orders of magnitude over other widely used simulation techniques.

Approximation theory↗