Search NASA⌕ Search

SEARCH · Search NASA

Results for “extrapolation method”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Quantitative Method for In Situ Pump-Beam Metrology in 4D Ultrafast Electron Microscopy

In this work, we report a method for measuring spot size and focusing conditions of the femtosecond (fs) excitation laser in situ at the specimen location in 4D ultrafast electron microscopy (UEM). The method makes use of threshold laser ablation behaviors of thin amorphous carbon membranes. For Gaussian beam profiles and for ablation threshold fluence values, we analytically derive expressions describing the relationship between ablated hole size and the actual laser spot size. Using these expressions, we developed experimental procedures for characterizing the shape and spot size of the pump beam at the specimen. We demonstrate the viability of the approach for incident excitation wavelengths of 343 nm and 515 nm, thus illustrating the applicability of the method to a range of optical wavelengths without modification. Further, we show that by measuring ablated hole size as a function of focusing condition, a full metrological characterization of the Gaussian beam propagation properties can be performed. Finally, we find good agreement for spot sizes determined with this method and with those determined by extrapolation from measurements taken outside the microscope column. Overall, this method is a simple, cost-effective means for accurate and precise determination of key pump-beam parameters in situ at the specimen location in UEM experiments.

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

Conditional Latent Diffusion for High-Resolution Prediction of Electrochemical Surface Morphology

A conditionally guided generative latent diffusion process that is trained on a set of experimental processing parameters and their associated resulting electron microscope images of the electrodeposition process is able to interpolate between processing parameters in a physically consistent way. Electrodeposition of rhenium with pulse and pulse-reverse waveforms is used as a model system, and the process is adaptable to other electrodeposition, electropolishing, or corrosion processes. The method is able to extrapolate, predicting estimates of material morphologies for experimental setups unseen in the training data. The results are demonstrated with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Nonergodic Ground-Motion Model for the San Francisco Bay Area for Small-Magnitude Earthquakes

ABSTRACT Recently, generative models have become a computationally efficient alternative to physics-based numerical simulations of ground motions. Neural networks can learn from existing ground-motion data to generate unobserved ground-motion data at new source and site locations. A key challenge with generative models is ensuring that predicted ground motions remain within a physically realistic range. For this purpose, we developed an empirical, nonergodic ground-motion model (GMM) for small-magnitude earthquakes in the San Francisco Bay area based on about 5000 recordings per component for Mw ≤ 4 earthquakes. The nonergodic GMM predicts spatially varying median source, site, and path effects for both the Fourier amplitude spectrum (FAS) and the Fourier phase derivative (a proxy for duration), as well as the corresponding epistemic uncertainty for each term. For FAS, our model shows above-average source and site effects in the western part of the region and below-average effects in the eastern part, with regional effects exhibiting larger spatial correlation lengths with increasing frequency. For duration, the source term is negligible for small-magnitude earthquakes, and the site term leads to site-specific variations up to 5 s. Path effects for FAS and duration depend on the source–site pair and are extrapolated spatially using recent methods for path-effect modeling. The aleatory variability of the within-site within-path residuals is similar to the variability found in previous studies for other regions. The nonergodic model provides two key contributions: first, median adjustment terms that are transferable to larger magnitude earthquakes, further reducing aleatory variability in probabilistic seismic hazard analysis; second, region-specific criteria for validating machine learning-based ground-motion generators to evaluate whether synthetic ground motions exhibit physically realistic source, site, and path effects.

Lacour, Maxime↗
DOE OSTI2024

Error mitigation, optimization, and extrapolation on a trapped-ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm’s sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH + molecule at 0.8 Å in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.8%, resulting in an energy estimate within –0.004 ± 0.04 hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Furthermore, our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Model-Free Probabilistic Forecasting of Nodal Voltages in Distribution Systems

As the penetration of distributed energy resources (DERs) into distribution systems increases, so does the interest in forecasting relevant system variables to help mitigate the associated challenges. One such challenge is the more frequent occurrence of excessive voltages in distribution systems with higher shares of DERs. Accurate and reliable estimates together with forecasts of system states (i.e., nodal voltages) will therefore play a key role in improving the utilization of these variable and uncertain sources while mitigating potential operational risks. Whilst recent literature has explored machine learning (ML) methods for voltage estimation and their extrapolation for a short-time period into the future, few have taken uncertainty quantification into account, and these methods have not yet been translated into operations. This paper discusses the advantages offered by probabilistic voltage forecasts and proposes a non-parametric Bayesian method suitable for forecasting nodal voltages at short-term time horizons while accounting for uncertainties in load and distributed photovoltaic (PV) generation. We demonstrate the value of the proposed Gaussian process (GP) model for a case study using historical forecasts and observation data.

distribution system↗
DOE OSTI2020

Updated External Exposure Dose Coefficients

In 2018, the Environmental Protection Agency (EPA) updated and expanded the Federal Guidance Report (FGR) No. 12 to No. 15; tabulating age-specific external exposure effective dose rate coefficients for 1,252 radionuclides in the air, water, and soil (EPA 2018). However, the EPA discovered errors in the tables of dose coefficients for soil which led to the report being retracted for correction. This led to the adoption of “a uniform method of data-smoothing and extrapolation of monoenergetic organ doses at low energies across all exposure pathways; the originally-published dose coefficients utilized different methods for each media type” (EPA 2019). This resulted in all the external exposure dose coefficients being updated and FGR 15 being republished in August 2019 with corrected tables.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Modeling and Simulation Development Pathways to Accelerating KP-FHR Licensing (Final Report)

This project assembles a strong U.S. industry and national laboratory team to complete scope of work. Kairos Power (KP), headquartered in Alameda, CA, is the leader of this effort and has built an internal team of highly competent engineers and managers with extensive combined experience in nuclear power, conventional power, product development, and licensing. INL, ANL, and LANL bring unique capabilities in advanced reactor R&D and licensing. The project funding source is the result of FOA No. 0001817, U. S. Industry Opportunities for Advanced Nuclear Technology Development. There has been on-going work and this Access Cooperative Research and Development Agreement (CRADA) will cover the remaining work scope of FOA 0001817. KP is implementing innovative strategies that can reduce the cost and accelerate the initial demonstration of the Kairos Power Fluoride-salt-cooled, High-temperature Reactor (KP-FHR) to meet the needs of the U.S. electricity market by 2030. Licensing of the KP-FHR could be significantly accelerated using advanced computing methods with sufficient predictive capabilities to be able to extrapolate potential response of the structure in different scenarios. However, currently used computational methods heavily rely on empirical fits and cannot be used for extrapolation. The scope focuses on improving the modeling capability in the NEAMS Grizzly structural mechanics code and the NEAMS BISON fuel performance code and the NEAMS SAM systems analysis code. This work leverages the expertise and know-how gathered in three DOE National Laboratories – INL, ANL, and LANL.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays

We present the first lattice QCD calculation of the universal axial γ W -box contribution □ γ W V A to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of | V u d | from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at □ γ W V A = 3.65 ( 7 ) lat ( 1 ) PT × 10 − 3 . Consequently, this yields a slightly higher value of | V u d | = 0.973 86 ( 11 ) exp ( 9 ) RC ( 27 ) NS , reducing the previous 2.1 σ tension with the CKM unitarity to 1.8 σ . Additionally, we calculate the vector γ W -box contribution to the axial charge g A , denoted as □ γ W V V , and explore its potential implications. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

FY25 status report on the addition of candidate materials in Class B Code Case

This report provides the time-dependent allowable stress calculation strategy leveraging the limited creep rupture tests data generated to support the allowable stress for 100,000 hours in American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), Section II, Part D. A variable confidence index procedure to extrapolate material properties to support 500,000 hours design life is discussed. Time-dependent allowable stresses for Class B component design and analysis are presented for Grade 1 and Grade 2 of Alloy 625. The presented data extrapolation and allowable stress calculation method will support new material addition using limited creep rupture data in the new ASME Boiler and BPVC, Section III, Division 5, Class B rules.

Part D↗
DOE OSTI2020

Decreasing wind speed extrapolation error via domain-specific feature extraction and selection

Abstract. Model uncertainty is a significant challenge in the wind energy industry and can lead to mischaracterization of millions of dollars' worth of wind resources. Machine learning methods, notably deep artificial neural networks (ANNs), are capable of modeling turbulent and chaotic systems and offer a promising tool to produce high-accuracy wind speed forecasts and extrapolations. This paper uses data collected by profiling Doppler lidars over three field campaigns to investigate the efficacy of using ANNs for wind speed vertical extrapolation in a variety of terrains, and it quantifies the role of domain knowledge in ANN extrapolation accuracy. A series of 11 meteorological parameters (features) are used as ANN inputs, and the resulting output accuracy is compared with that of both standard log-law and power-law extrapolations. It is found that extracted nondimensional inputs, namely turbulence intensity, current wind speed, and previous wind speed, are the features that most reliably improve the ANN's accuracy, providing up to a 65 % and 52 % increase in extrapolation accuracy over log-law and power-law predictions, respectively. The volume of input data is also deemed important for achieving robust results. One test case is analyzed in depth using dimensional and nondimensional features, showing that the feature nondimensionalization drastically improves network accuracy and robustness for sparsely sampled atmospheric cases.

17 WIND ENERGY↗
DOE OSTI2020

Microscopic calculations of nuclear level densities with the Lanczos method

A new method for computing the density of states in nuclei making use of an extrapolated form of the tridiagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire Lanczos matrix can be predicted from just four Lanczos iterations. The extrapolated Lanczos matrix (ELM) approach provides for an accurate computation of the density of states described within the configuration space, which, in some cases, is sufficient to accurately calculate the density of states at, or near, the neutron separation energy. Comparisons between theory and experiment are shown for $^{57}Fe$, $^{74}Ge$, and $^6Ge$. In addition, we show results for the J -dependence of moments and the level density for these three nuclei.

Shell model↗
DOE OSTI2021

Extending quantum probabilistic error cancellation by noise scaling

Here, we propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device’s noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this Letter, we present the first study of the convergence of eigenvector continuation. In order to perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between nonorthogonal vectors appearing at different orders in perturbation theory. From our analysis we can predict how eigenvector continuation converges both inside and outside the radius of convergence of perturbation theory. Further, while eigenvector continuation is a nonperturbative method, we show that its rate of convergence can be deduced from power series expansions of the eigenvectors. Our results also yield new insights into the nature of divergences in perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

First-Principles Treatment of Vibrational Broadening in X-Ray Excited Valence Band Spectra for n-SrTiO 3 (001)

The valence band maximum (VBM) is an important quantity for semiconductors as it locates the Fermi level relative to the band edge. Accurate measurement of this quantity in near-surface regions of semiconductors by photoemission is a first step toward determining the electronic properties of heterostructures involving these materials. While extrapolating the leading edge of the valence band to the energy axis in photoemission spectra is a widely used way to find the VBM, this method can be ambiguous if the leading edge exhibits multiple slopes. Another way to determine the VBM is to fit the leading edge to an appropriately broadened, cross-section modulated theoretical density of states (DOS). Three kinds of broadening that should be included for maximum accuracy are those due to: (1) finite instrumental resolution, (2) valence hole lifetime, and (3) vibrational excitations. While steps (1) and (2) are straightforward to implement, (3) is more difficult because the appropriate amount of broadening is not known a priori. Here, we demonstrate that explicit inclusion of vibrational broadening using ab initio molecular dynamics facilitates accurate VBM determination for n-SrTiO 3 (001). The total DOS is constructed by summing time-averaged projections at elevated temperature onto s - , p - , and d orbitals for the constituent atoms and modulating with the associated photoemission cross sections. Subsequent convolutions of the total DOS, first with a Gaussian of width equal to the experimental energy resolution and second with a Lorentzian to simulate valence hole lifetime effects, yield line shapes that reproduce the experimental leading edges rather well. The VBM is then given by the energy at which the vibrationally broadened total DOS (prior to the convolutions) goes to zero. The VBMs generated by this method quantitatively agree with those resulting from extrapolating from the middle of the measured leading edge for SrTiO 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Materials Characterization, Prediction, and Control Project: Characterization of 316L Stainless Steel after Solid Phase Processing using Ultrasonic NDE Method

The Pacific Northwest National Laboratory undertook the Materials Characterization, Prediction, and Control Laboratory Directed Research and Development Project to advance understanding of nuclear material processing and enable multifold acceleration in the development and qualification of new material systems produced via advanced manufacturing methods, such as solid phase processing, for use in national security and advanced energy applications (Smith 2021). A motivation of the Materials Characterization, Prediction, and Control Project was to demonstrate ultrasonic testing as a nondestructive evaluation method to complement traditional destructive methods for characterizing material microstructure with emphasis on grain size determination using a method that may have future applications for real-time inline process monitoring. The objective of the work described in this report is to establish the process and an analysis method for measuring grain sizes of polycrystalline metals with ultrafine grains using ultrasonic shear wave backscattering, building on prior studies on coarser-grained material. The work involves five tasks: Measured ultrasonic backscattering experimentally for a series of 316L stainless steel specimens with various grain sizes made by friction stir processing. Calculated ultrasonic backscattering coefficients from experimental data based on a physical measurement model. Measured ground truth grain sizes of the specimens from electron backscatter diffraction grain boundary images using a generalization of the ASTM E112 (ASTM 2021) intercept method. Built a curve of ultrasonic backscattering coefficients versus the ground truth intercept-based grain sizes to determine the correlation between mean grain sizes and ultrasonic measurements. Demonstrated the ability of using the correlation curve to deduce grain sizes with measured ultrasonic backscattering coefficients for a few 316L stainless steel specimens whose grain sizes were unknown beforehand but were targeted to be an extrapolation to larger grain sizes than used to formulate the correlation curves. Experimental procedures and computational algorithms are developed and validated for these tasks. This work establishes an ultrasonic technique for characterizing material microstructure with ultrafine grains that are often resulted by solid-phase processing. The technique is nondestructive, and it has the potential to be used for real time inline process monitoring. This work successfully demonstrates the viability of an ultrasonic nondestructive evaluation method for microstructural characterization of material having ultrafine grain structure (as small as 1?mm) and produced by an advanced manufacturing method. This includes a demonstration of the method to extrapolate to other conditions. While not demonstrated here, the method is expected to be viable for in-line, or near-inline, process monitoring in advanced manufacturing applications with suitable consideration for access of instrumentation to the material being manufactured.

316 L Stainless Steel↗
DOE OSTI2023

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH) 4 H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ΔE estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree–Fock included (0%–54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ΔE is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn–Sham orbitals gives results within 4–11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ~5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗