Search NASA⌕ Search

SEARCH · Search NASA

Results for “interpolated”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks

Generative Adversarial Networks (GANs) are becoming popular choices for unsupervised learning. At the same time there is a concerted effort in the machine learning community to expand the range of tasks in which learning can be applied as well as to utilize methods from other disciplines to accelerate learning. With this in mind, in the current work we suggest ways to enforce given constraints in the output of a GAN both for interpolation and extrapolation. The two cases need to be treated differently. For the case of interpolation, the incorporation of constraints is built into the training of the GAN. The incorporation of the constraints respects the primary game-theoretic setup of a GAN so it can be combined with existing algorithms. However, it can exacerbate the problem of instability during training that is well-known for GANs. We suggest adding small noise to the constraints as a simple remedy that has performed well in our numerical experiments. The case of extrapolation (prediction) is more involved. First, we employ a modified interpolation training process that uses noisy data but does {\it not} necessarily enforce the constraints during training. Second, the resulting modified interpolator is used for extrapolation where the constraints are enforced after each step through projection on the space of constraints.

Stinis, Panagiotis↗
DOE OSTI2021

Bias Characterization, Vertical Interpolation, and Horizontal Interpolation for Distributed Wind Siting Using Mesoscale Wind Resource Estimates

Much like their counterparts in utility-scale wind energy, developers of industrial, small-scale and distributed wind turbine deployments need to understand and accurately characterize the wind resource to properly assess the power generation and financial ramifications during siting and planning. National Renewable Energy Laboratory’s WIND (Wind Integration National Dataset) Toolkit (WTK) provides a best-in-class wind resource dataset generated using the Weather Research and Forecasting (WRF) model. This dataset includes parameters such as the wind speed, wind direction, and temperature at various heights, plus atmospheric stability near the surface. This data is available at 2-km spatial resolution and five-minute temporal resolution across 7 years, from 2007 to 2013 through a publicly accessible API interface. The Tools Assessing Performance (TAP) project seeks to extend this dataset to allow long term resource estimates and leverage it to better equip distributed wind equipment manufacturers, owner-operators, and installation professionals with better tools for practical siting applications. In this report, we present the results from our investigation within the TAP project focused on characterization of bias in WTK-based wind speed estimates and evaluation of vertical and horizontal interpolation techniques. We discuss the tradeoffs between different techniques and their combinations, as well as describe the lower bounds we determine for the studied validation errors. While the specific estimates we present are specific to WTK and the validation dataset we have chosen for this investigation (NREL's Wind Resource Meteorological Database), the overall analysis and the studied techniques are general enough to be applied to a broader set of wind datasets, both simulation-based and observational.

17 WIND ENERGY↗
DOE OSTI2021

Clock model interpolation and symmetry breaking in O(2) models

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma=0$ and to the extended $q$-state clock model when $\gamma\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

Hostetler, Leon↗
DOE OSTI2021

Discrete Empirical Interpolation Method Based Dynamic Load Model Reduction

Dynamic load models add significant complexity to bulk power system time-domain simulations. The complexity is due to the large number of ordinary differential equations (ODEs) introduced by the dynamic load components such as induction motors. It is challenging to derive reduced-order models (ROMs) for dynamic loads due to the nonlinear functions in their governing equations. This paper applies the discrete empirical interpolation method enhanced proper orthogonal decomposition (DEIM-POD) to approximate the full dynamic load model with the ROM that minimizes the projection error of the nonlinear functions in dynamic load ODEs onto their dominant modes. This approach only requires evaluation of nonlinear functions at selected observation points. The observation points selected by DEIM also provide information for screening critical load buses where dynamic load model parameters contribute the most to the accuracy of ROM across multiple contingencies. The proposed approach is validated on IEEE 9-bus, WECC 179-bus and 2384-bus Polish systems.

bulk power system↗
DOE OSTI2024

ninterp: N-dimensional interpolation Rust crate [SWR-25-25]

The ninterp crate provides multivariate interpolation over a regular, sorted, nonrepeating grid of any dimensionality. A variety of interpolation strategies are implemented, however more are likely to be added. Extrapolation beyond the range of the supplied coordinates is supported for 1-D linear interpolators, using the slope of the nearby points. There are hard-coded interpolators for lower dimensionalities (up to N = 3) for better runtime performance. All interpolation is handled through instances of the Interpolator enum, with the selected tuple variant containing relevant data. Interpolation is executed by calling Interpolator::interpolate.

Carow, Kyle↗
DOE OSTI2018

Bicubic partially blended rational fractal surface for a constrained interpolation problem

This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Interpolation of compound semiconductor alloy parameters from those of their constituents

Several methods have been proposed for interpolation of the value of physical parameters of quaternary alloys from those of their constituent ternary and binary sub-alloys. These expressions agree when non-linear bowing terms are not required; they differ in how the bowing terms of the bounding ternaries should be utilized. Common interpolation expressions for quaternaries can be generalized into two groups: (1) those that use a linear interpolation of the nearest ternary parameter values and (2) those that interpolate over binary values with a bowing term derived from the bounding ternaries. The second group of methods is equivalent to a polynomial expansion over the alloy’s interpolation space. For compound semiconductor alloys, the geometry of the composition space is the direct sum of the group-III and group-V mixture sub-spaces. The mixture sub-spaces are best described using barycentric coordinates on a regular simplex. A general polynomial expansion of the value of an alloy parameter using barycentric coordinates for the group-III and group-V simplex spaces is described along with an algorithm to generate interpolation expressions for alloys with arbitrary numbers of elements, including quinary and senary alloys. It is shown that a polynomial expansion produces values in closer agreement with the direct gap of quaternaries lattice-matched to common substrates than do approaches using an interpolation of the ternary values, despite a prominent recommendation to the contrary. Finally, a quaternary correction term is described that improves the predicted direct bandgap energies of GaInAsSb for compositions near those lattice matched to InP, InAs, and GaSb.

Olesberg, Jonathon T. [Sandia National Laboratorie↗
DOE OSTI2024

Implementation of High Temperature and Pressure fluid property interpolation tables

This document describes the use of module property_interpolate by John Doherty (Doherty,2006). The document “Fast Lookup of CO 2 Properties” describes the numerical details associated with lookup table. Rajeh Pawar modified property_interpolate for easier implementation in the FEHM code. George Zyvoloski modified the package to produce tables for water and air at very high temperatures and pressures. He also modified the auxiliary codes(drivers) to use newer datasets from the National Institute of Standards and Technology. We note here that within the files associated with FEHM there three property_interpolate modules. They are interpolate_2a.f90 (water), interpolate_2b.f90 (air) , and interpolate_2c.f90(CO 2 ). The interpolate_2c module is different than the earlier module produced by Rajeh Pawar in that it includes high temperature and pressure data. While FEHM has a number of fluid physics modules, this document will describe only the software and algorithms associated with water, water vapor, and heat (WH).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j ). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j ). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j ) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min ,T max ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238 U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238 U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A Method of Moments Wide Band Adaptive Rational Interpolation Method for High-Quality Factor Resonant Cavities

A new adaptive rational interpolation method is proposed to obtain the wideband frequency response of a resonant cavity simulated with the method of moments (MoM). This interpolation method uses both the Loewner matrix to construct a rational expression for the solution vector of MoM’s matrix system and an error estimator generated by the solution vectors and their derivatives. This error estimator is implemented in the adaptive procedure to gain a minimum set of frequencies and solution vectors required in the interpolation. The resulting set of frequencies and solution vectors is applied to interpolate other system variables, such as shielding effectiveness and input impedance. Here numerical results of a slotted cylindrical cavity supporting high-quality factor resonances are presented, showing that the new rational interpolation method is accurate and efficient in interpolating the complicated resonant response of the solution vector functions.

42 ENGINEERING↗
DOE OSTI2023

Coordinate-Based Seismic Interpolation in Irregular Land Survey: A Deep Internal Learning Approach

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Preprocessing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data in such cases. Recently, deep learning has been used to address the trace interpolation problem at the expense of large amounts of training data to adequately represent typical seismic events. Nonetheless, most research in this area has focused on trace reconstruction, with little attention having been devoted to shot interpolation. Furthermore, existing methods assume regularly spaced receivers/sources failing in approximating seismic data from real (irregular) surveys. This work presents a novel shot gather interpolation approach which uses a continuous coordinate-based representation of the acquired seismic wavefield parameterized by a neural network. The proposed unsupervised approach, which we call coordinate-based seismic interpolation (CoBSI), enables the prediction of specific seismic characteristics in irregular land surveys without using external data during neural network training. Importantly, experimental results on real and synthetic 3-D data validate the ability of the proposed method to estimate continuous smooth seismic events in the time-space and frequency-wavenumber domains, improving sparsity or low-rank-based interpolation methods.

58 GEOSCIENCES↗
DOE OSTI2023

Logarithm-Based Methods for Interpolating Quaternion Time Series

In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C 2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables $\theta$ and $\hat{n}$ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Estimation and Visualization of Isosurface Uncertainty from Linear and High-Order Interpolation Methods

Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is easy to implement, it has limitations when the underlying data is complex and high-order, which is the case for most real-world data. Linear interpolation can output vertices at the wrong location. Its inability to deal with sharp features and features smaller than grid cells can lead to an incorrect isosurface with holes and broken pieces. Despite these limitations, isosurface visualizations typically do not include insight into the spatial location and the magnitude of these errors. We utilize high-order interpolation methods with MC algorithms and interactive visualization to highlight these uncertainties. Our visualization tool helps identify the regions of high interpolation errors. It also allows users to query local areas for details and compare the differences between isosurfaces from different interpolation methods. In addition, we employ high-order methods to identify and reconstruct possible features that linear methods cannot detect. We showcase how our visualization tool helps explore and understand the extracted isosurface errors through synthetic and real-world data.

Ouermi, Timbwaoga↗
DOE OSTI2017

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗