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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Trigonometric Interpolation and Quadrature in Perturbed Points

The trigonometric interpolants to a periodic function f in equispaced points converge if f is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if f is continuous. What if the points are perturbed? With equispaced grid spacing h, let each point be perturbed by an arbitrary amount <= alpha h, where alpha is an element of[0, 1/2) is a fixed constant. The Kadec 1/4 theorem of sampling theory suggests there may be trouble for alpha >= 1/4. We show that convergence of both the interpolants and the quadrature estimates is guaranteed for all alpha < 1/2 if f is twice continuously differentiable, with the convergence rate depending on the smoothness of f. More precisely, it is enough for f to have 4 alpha derivatives in a certain sense, and we conjecture that 2 alpha derivatives are enough. Connections with the Fejer-Kalmar theorem are discussed.

Fej´er–Kalm´ar theorem↗
DOE OSTI2021

The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication

Understanding flood probabilities is essential to making sound decisions about flood-risk management. Many people rely on flood probability maps to inform decisions about purchasing flood insurance, buying or selling real-estate, flood-proofing a house, or managing floodplain development. Current flood probability maps typically use flood zones (for example the 1 in 100 or 1 in 500-year flood zones) to communicate flooding probabilities. However, this choice of communication format can miss important details and lead to biased risk assessments. Here we develop, test, and demonstrate the FLOod Probability Interpolation Tool (FLOPIT). FLOPIT interpolates flood probabilities between water surface elevation to produce continuous flood-probability maps. FLOPIT uses water surface elevation inundation maps for at least two return periods and creates Annual Exceedance Probability (AEP) as well as inundation maps for new return levels. Potential advantages of FLOPIT include being open-source, relatively easy to implement, capable of creating inundation maps from agencies other than FEMA, and applicable to locations where FEMA published flood inundation maps but not flood probability. Using publicly available data from the Federal Emergency Management Agency (FEMA) flood risk databases as well as state and national datasets, we produce continuous flood-probability maps at three example locations in the United States: Houston (TX), Muncy (PA), and Selinsgrove (PA). We find that the discrete flood zones generally communicate substantially lower flood probabilities than the continuous estimates.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.

uncertainty quantification↗
NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.

uncertainty quantification↗
NASA NTRS2023

On Hermite Interpolation using Bernstein Polynomials for Trajectory Generation

This work presents a solution to the two-point Hermite interpolation problem using Bernstein polynomials. The Hermite interpolation problem is of particular interest in aerospace applications where boundary conditions for trajectories often specify derivative constraints. In the examples shown, a trajectory will be generated between an initial condition and a final condition. For example, a trajectory is generated that connects an aircraft’s current position and velocity with a point on the runway at a desired landing velocity. The numerical stability of the proposed algorithms is analyzed empirically.

Bezier curves↗
DOE OSTI2015

Interpolating the Coulomb phase of little string theory

We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. As a result, we also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Spatiotemporal interpolation of air pollutants in the Greater Cairo and the Delta, Egypt

Highlights: • Data from network of monitoring stations in Egypt are used for studying SO{sub 2}, NO{sub 2}, and PM{sub 10.} • Trans-Gaussian Spatiotemporal kriging is used as a spatiotemporal interpolation method. • The whole area under study is suffering from high values of PM{sub 10} throughout 2015. • For NO{sub 2} and SO{sub 2}, the highest value is noticed in February. • Concerns must be given to the monitoring network to improve the prediction precision. This paper analyses the spatiotemporal variability of air pollutants in Egypt using monthly averages from the air quality monitoring network from 2011 to 2015. Particulate Matters (PM{sub 10}) Nitrogen Dioxide (NO{sub 2}) and Sulfur Dioxide (SO{sub 2}), measured by the monitoring stations network are studied. A log transformation is applied for the three pollutants to achieve normality. The sum-metric function is utilized for modelling the spatiotemporal variogram as it gave the smallest Mean Squared Error (MSE) compared to other forms namely separable, metric, and product sum models. Therefore, employing the gstat package in R together with the trans-Gaussian spatiotemporal kriging, the maps are generated for the interpolated surfaces for the monthly averages of 2015 and the corresponding standard error values. These maps will help the decision maker to understand and visualize the spatial and temporal variability of the measured pollutants and hence undertake the necessary policies and decisions. The results show that the down town area has the highest pollutants levels. As concerns the temporal dimension, the highest values are depicted during the month of February as compared to the rest of the year. Furthermore, Egypt is suffering from a serious PM{sub 10} problem for the area and period under study that extremely exceed the WHO and Egyptian guidelines.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Graph interpolating activation improves both natural and robust accuracies in data-efficient deep learning

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning (DL) research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high-dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace–Beltrami equation on a high-dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation integrates the advantages of both deep learning and manifold learning. Compared to the conventional DNNs with the softmax function as output activation, the new framework demonstrates the following major advantages: First, it is better applicable to data-efficient learning in which we train high capacity DNNs without using a large number of training data. Second, it remarkably improves both natural accuracy on the clean images and robust accuracy on the adversarial images crafted by both white-box and black-box adversarial attacks. Third, it is a natural choice for semi-supervised learning. This paper is a significant extension of our earlier work published in NeurIPS, 2018. For reproducibility, the code is available at https://github.com/BaoWangMath/DNN-DataDependentActivation .

Mathematics↗
DOE OSTI2021

Dimensional Interpolation for Random Walk

In this work, we employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Grassmann interpolation method for spin-unrestricted open-shell systems

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice—one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg–Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Chemistry↗
DOE OSTI2025

Kinematically enhanced interpolating operators for boosted hadrons

We propose to use interpolating operators for lattice quantum chromodynamics calculations of highly boosted pions and nucleons with kinematically enhanced ground-state overlap factors at large momentum. Because this kinematic enhancement applies to the signal but not the variance of the correlation function, these interpolating operators can achieve better signal-to-noise ratios at large momentum. We perform proof-of-principle calculations with boosted pions and nucleons using close-to-physical and larger quark masses to explore the utility of our proposal. Results for effective energies and matrix elements, as well as Lanczos ground-state energy estimators, are consistent with theoretical expectations for signal-to-noise improvement at large momenta.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Chiral properties of the nucleon interpolating current and θ-dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j 1 and j 2 , only two linear combinations j 1 ± j 2 transform covariantly under the anomalous U⁢(1) A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (d n,p ) induced by θ, and the nucleon magnetic moments (μ n,p ), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, d n,p /μ n,p , are numerically consistent, and reflect the required physical dependence on θ.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Tuning the Interpolation Basis in a Multigrid Decomposition for Local Error Control

In the compression of scientific data, error-controlled compressors enable to considerably decrease the size of the dataset while maintaining adequate levels of accuracy. In this paper, we note that multi-level refactoring scheme such as MGARD i) rely on an approximation of the data based on the interpolation of coefficients, ii) estimate the resulting error with global metrics on the dataset. To improve on these two aspects, we propose a method that aims to divide the original dataset into blocks based on their smoothness and refactors each block separately with the most relevant interpolation order. We show the relevance of such a method on tailored datasets and the benefits and challenges when applying it to large scientific data.

Vidal, Nicolas [ORNL]↗
DOE OSTI2016

Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation

Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a two-dimensional image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, can enable high speed data acquisition and minimize sample damage caused by the electron beam. In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the nonlocal redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a “prior model” for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new nonlocal means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Combined Dimensional and Topology Optimization of Synchronous Machine Rotors Using a Material Density Interpolation Method

This article presents a magneto-structural combined dimensional and topology optimization technique for interior permanent magnet synchronous machine (IPMSM) and wound field synchronous machine (WFSM) rotors. Dimensional changes to the permanent magnet (PM) and rotor winding location or size are accomplished by interpolating or projecting a smoothed Heaviside rectangular function representing the presence of PM material onto the IPMSM rotor design domain mesh, whereas the presence of copper material for WFSM rotor is interpolated in the same manner. A density based Solid Isotropic Material with Penalization (SIMP) topology optimization approach is then used to vary the presence of electrical steel in mesh elements to form flux barriers around the PM. The proposed method enforces a defined shape for the PM without requiring the mesh in the design domain to be deformed. Four examples are presented to demonstrate the technique: Two flat bar IPMSM, one V-shaped IPMSM, and a WFSM. Here, a comparative study is performed on one of the flat bar IPMSMs using Metamodel of Optimal Prognosis (MOP) based method.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH ↗
DOE OSTI2015

Interpolating Low Time-Resolution Forecast Data

Methodology that interpolates low time-resolution data (e.g., hourly) to high time-resolution (e.g., minutely) with variability patterns extracted from historical records. Magnitude of the variability inserted into the low time resolution data can be adjusted according to the installed capacity represented by the low time-resolution data compared to that by historical records. This approach enables detailed analysis of the impacts from wind and solar on power system intra-hour operations and balancing reserve requirements even with only hourly data. It also allows convenient creation of high resolution wind or solar generation data with various degree of variability to investigate their operational impacts. The methodology comprises of the following steps: 1. Smooth the historical data (set A) with an appropriate window length l to get its trend (set B); l can be a fraction of an hour (e.g., 15 minutes) or longer than an hour, of which the length of the variability patterns will be; 2. Extract the variable component (set C) of historical data by subtracting the smooth trend from it, i.e. set C = set A - set B 3. For each window length l of the variable component data set, find the average value x (will call it base component) of the corresponding window of the historical data set; 4. Define a series of segments (set D) that the values of data will be grouped into, e.g. (0, 0.1), (0.1, 0.2), ..., (0.9, 1.0) after normalization; Link each variability pattern to a data segment based on its corresponding base component x; after this step, each data segment should be linked to multiple variability patterns after this step; 5. Use spline function to interpolate the low time-resolution forecast data (set E) to become a high time-resolution smooth curve (set F); 6. Based on the window length l , calculate the average value y in each window length of set F; find the data segment that y belongs to; then randomly select one of the variability patterns linked to this data segment; 7. Add the selected variability pattern in each window to set F to get the high time-resolution data (set G) with variability observed from historical data set A; a coefficient k can be multiplied to the selected variability pattern to reflect the potential difference in variability between forecast set E and historical data set A caused by installation capacity and other factors. 8. After set G is constructed, variability statistics can be checked for set A and set G for comparison. Adjust the coefficient k if necessary to achieve desired variability in the reconstructed data.

Lu, Shuai↗
DOE OSTI2022

Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman D_0 D 0 function, and the two-loop self-energy master integral M. We find that in low dimensions (d = 3), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions (d=5, 6, 9) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.

97 MATHEMATICS AND COMPUTING↗