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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Extrapolation limitations of multilayer feedforward neural networks

The limitations of backpropagation used as a function extrapolator were investigated. Four common functions were used to investigate the network's extrapolation capability. The purpose of the experiment was to determine whether neural networks are capable of extrapolation and, if so, to determine the range for which networks can extrapolate. The authors show that neural networks cannot extrapolate and offer an explanation to support this result.

Haley, Pamela J.↗
NASA NTRS1992

The Extrapolation of Elementary Sequences

We study sequence extrapolation as a stream-learning problem. Input examples are a stream of data elements of the same type (integers, strings, etc.), and the problem is to construct a hypothesis that both explains the observed sequence of examples and extrapolates the rest of the stream. A primary objective -- and one that distinguishes this work from previous extrapolation algorithms -- is that the same algorithm be able to extrapolate sequences over a variety of different types, including integers, strings, and trees. We define a generous family of constructive data types, and define as our learning bias a stream language called elementary stream descriptions. We then give an algorithm that extrapolates elementary descriptions over constructive datatypes and prove that it learns correctly. For freely-generated types, we prove a polynomial time bound on descriptions of bounded complexity. An especially interesting feature of this work is the ability to provide quantitative measures of confidence in competing hypotheses, using a Bayesian model of prediction.

Laird, Philip↗
NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗
NASA NTRS2007

The Extrapolation of High Altitude Solar Cell I(V) Characteristics to AM0

The high altitude aircraft method has been used at NASA GRC since the early 1960's to calibrate solar cell short circuit current, ISC, to Air Mass Zero (AMO). This method extrapolates ISC to AM0 via the Langley plot method, a logarithmic extrapolation to 0 air mass, and includes corrections for the varying Earth-Sun distance to 1.0 AU and compensating for the non-uniform ozone distribution in the atmosphere. However, other characteristics of the solar cell I(V) curve do not extrapolate in the same way. Another approach is needed to extrapolate VOC and the maximum power point (PMAX) to AM0 illumination. As part of the high altitude aircraft method, VOC and PMAX can be obtained as ISC changes during the flight. These values can then the extrapolated, sometimes interpolated, to the ISC(AM0) value. This approach should be valid as long as the shape of the solar spectra in the stratosphere does not change too much from AMO. As a feasibility check, the results are compared to AMO I(V) curves obtained using the NASA GRC X25 based multi-source simulator. This paper investigates the approach on both multi-junction solar cells and sub-cells.

Snyder, David B.↗
DOE OSTI2025

Combining physics-based and data-driven models for quantitatively accurate plasma profile prediction that extrapolates well; with application to DIII-D, AUG, and ITER tokamaks

For design, scenario planning, and control, ITER and all other envisioned tokamaks rely on a variety of statistical and physics-based models to extrapolate to unseen regimes; most notably from low plasma current to high. A 'meta-learning' methodology for combining the accuracy of data-driven models with the generalizability of physics-based models is described and tested, yielding a 5–10 percent improvement in performance beyond either alone for the task of extrapolating time-dependent plasma profile prediction from low- to high- plasma current DIII-D tokamak discharges. Meanwhile, it is shown that both machine learning models extrapolated far-distribution and state-of-the-art 'physics-based' profile predictors fare worse than merely assuming plasma profiles do not change from their initial values. Finally, a variety of other mechanisms for helping data-driven models generalize—transfer learning, adding contextual information from physics simulators, and adding data from the ASDEX Upgrade tokamak—are attempted for similar extrapolation tasks but, in the methodology used in this paper, yield no significant improvement beyond simple data-driven models. Results are summarized in figures 15 and 16.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting

Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time.

Deep learning↗
DOE OSTI2026

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES↗
DOE OSTI2026

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 OSTI2024

Quantum error mitigation by layerwise Richardson extrapolation

A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing layerwise Richardson extrapolation (LRE), an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. Furthermore, we provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Toward scalable bound-to-resonance extrapolations for few- and many-body systems

In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. Here, we first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model.

Ab initio calculations↗
DOE OSTI2024

Extrapolation of Type Ia Supernova Spectra into the Near-infrared Using Principal Component Analysis

Abstract We present a method of extrapolating the spectroscopic behavior of Type Ia supernovae (SNe Ia) in the near-infrared (NIR) wavelength regime up to 2.30 μ m using optical spectroscopy. Such a process is useful for accurately estimating K-corrections and other photometric quantities of SNe Ia in the NIR. A principal component analysis is performed on data consisting of Carnegie Supernova Project I & II optical and NIR FIRE spectra to produce models capable of making these extrapolations. This method differs from previous spectral template methods by not parameterizing models strictly by photometric light-curve properties of SNe Ia, allowing for more flexibility of the resulting extrapolated NIR flux. A difference of around −3.1% to −2.7% in the total integrated NIR flux between these extrapolations and the observations is seen here for most test cases including Branch core-normal and shallow-silicon subtypes. However, larger deviations from the observation are found for other tests, likely due to the limited high-velocity and broad-line SNe Ia in the training sample. Maximum-light principal components are shown to allow for spectroscopic predictions of the color-stretch light-curve parameter, s BV , within approximately ±0.1 units of the value measured with photometry. We also show these results compare well with NIR templates, although in most cases the templates are marginally more fitting to observations, illustrating a need for more concurrent optical+NIR spectroscopic observations to truly understand the diversity of SNe Ia in the NIR.

Astronomy & Astrophysics↗
NASA NTRS1982

Measurement accuracies in band-limited extrapolation

The problem of numerical instability associated with extrapolation algorithms is addressed. An attempt is made to estimate the bounds for the acceptable errors and to place a ceiling on the measurement accuracy and computational accuracy needed for the extrapolation. It is shown that in band limited (or visible angle limited) extrapolation the larger effective aperture L' that can be realized from a finite aperture L by over sampling is a function of the accuracy of measurements. It is shown that for sampling in the interval L/b absolute value of xL, b1 the signal must be known within an error e sub N given by e sub N squared approximately = 1/4(2kL') cubed (e/8b L/L')(2kL') where L is the physical aperture, L' is the extrapolated aperture, and k = 2pi lambda.

Kritikos, H. N.↗
NASA NTRS1984

An analysis of shock coalescence including three-dimensional effects with application to sonic boom extrapolation

A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack.

Darden, C. M.↗
NASA NTRS1984

Cosmogony as an extrapolation of magnetospheric research

A theory of the origin and evolution of the Solar System which considered electromagnetic forces and plasma effects is revised in light of information supplied by space research. In situ measurements in the magnetospheres and solar wind can be extrapolated outwards in space, to interstellar clouds, and backwards in time, to the formation of the solar system. The first extrapolation leads to a revision of cloud properties essential for the early phases in the formation of stars and solar nebulae. The latter extrapolation facilitates analysis of the cosmogonic processes by extrapolation of magnetospheric phenomena. Pioneer-Voyager observations of the Saturnian rings indicate that essential parts of their structure are fossils from cosmogonic times. By using detailed information from these space missions, it is possible to reconstruct events 4 to 5 billion years ago with an accuracy of a few percent.

Alfven, H.↗
NASA NTRS1984

Cosmogony as an extrapolation of magnetospheric research

A theory of the origin and evolution of the Solar System which considered electromagnetic forces and plasma effects is revised in light of information supplied by space research. In situ measurements in the magnetospheres and solar wind can be extrapolated outwards in space, to interstellar clouds, and backwards in time, to the formation of the solar system. The first extrapolation leads to a revision of cloud properties essential for the early phases in the formation of stars and solar nebulae. The latter extrapolation facilitates analysis of the cosmogonic processes by extrapolation of magnetospheric phenomena. Pioneer-Voyager observations of the Saturnian rings indicate that essential parts of their structure are fossils from cosmogonic times. By using detailed information from these space missions, it is possible to reconstruct events 4 to 5 billion years ago with an accuracy of a few percent.

Alfven, H.↗
NASA NTRS1992

Extrapolation procedures in Mott electron polarimetry

In standard Mott electron polarimetry using thin gold film targets, extrapolation procedures must be used to reduce the experimentally measured asymmetries A to the values they would have for scattering from single atoms. These extrapolations involve the dependent of A on either the gold film thickness or the maximum detected electron energy loss in the target. A concentric cylindrical-electrode Mott polarimeter, has been used to study and compare these two types of extrapolations over the electron energy range 20-100 keV. The potential systematic errors which can result from such procedures are analyzed in detail, particularly with regard to the use of various fitting functions in thickness extrapolations, and the failure of perfect energy-loss discrimination to yield accurate polarizations when thick foils are used.

Gay, T. J.↗
NASA NTRS1998

Atomization Energies of SO and SO2; Basis Set Extrapolation Revisted

The addition of tight functions to sulphur and extrapolation to the complete basis set limit are required to obtain accurate atomization energies. Six different extrapolation procedures are tried. The best atomization energies come from the series of basis sets that yield the most consistent results for all extrapolation techniques. In the variable alpha approach, alpha values larger than 4.5 or smaller than 3, appear to suggest that the extrapolation may not be reliable. It does not appear possible to determine a reliable basis set series using only the triple and quadruple zeta based sets. The scalar relativistic effects reduce the atomization of SO and SO2 by 0.34 and 0.81 kcal/mol, respectively, and clearly must be accounted for if a highly accurate atomization energy is to be computed. The magnitude of the core-valence (CV) contribution to the atomization is affected by missing diffuse valence functions. The CV contribution is much more stable if basis set superposition errors are accounted for. A similar study of SF, SF(+), and SF6 shows that the best family of basis sets varies with the nature of the S bonding.

Bauschlicher, Charles W., Jr.↗