Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTERPOLATION”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Accelerating Optical Absorption Spectra and Exciton Energy Computation via Interpolative Separable Density Fitting

© Springer International Publishing AG, part of Springer Nature 2018. We present an efficient way to solve the Bethe–Salpeter equation (BSE), a method for the computation of optical absorption spectra in molecules and solids that includes electron–hole interactions. Standard approaches to construct and diagonalize the Bethe–Salpeter Hamiltonian require at least (Formula Presented) operations, where Neis the number of electrons in the system, limiting its application to smaller systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare exchange and screened direct operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to (Formula Presented) with a much smaller pre-constant, and allows for a faster solution of the BSE. Here, we implement the ISDF method for BSE calculations within the Tamm–Dancoff approximation (TDA) in the BerkeleyGW software package. We show that this novel approach accurately reproduces exciton energies and optical absorption spectra in molecules and solids with a significantly reduced computational cost.

Hu, W↗
DOE OSTI2020

Time-step dependent force interpolation scheme for suppressing numerical Cherenkov instability in relativistic particle-in-cell simulations

The WT scheme, a piecewise polynomial force interpolation scheme with time-step dependency, is proposed in this paper for relativistic particle-in-cell (PIC) simulations. The WT scheme removes the lowest order numerical Cherenkov instability (NCI) growth rate for arbitrary time steps allowed by the Courant condition. While NCI from higher order resonances is still present, the numerical tests show that for smaller time steps, the numerical instability grows much slower than using the optimal time step found in previous studies. The WT scheme is efficient for improving the quality and flexibility of relativistic PIC simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Beyond interpolation: Physics-inspired gating transformers for extrapolating irradiation conditions to novel nuclear fuels

The qualification of advanced nuclear fuels relies on irradiation experiments in test reactors that emulate commercial conditions. Designing these tests requires accurate prediction of key irradiation quantities, particularly heat generation rate and burnup, yet obtaining them typically involves computationally expensive multi-step simulation workflows. We propose a physics-inspired gating transformer (PIGT) that integrates an inverse-square, distance-based attenuation into the encoder representation to bias attention toward physically relevant spatial relationships while retaining data-driven flexibility. Using MiniFuel irradiation data from the High Flux Isotope Reactor at Oak Ridge National Laboratory, we benchmark against ensemble methods, feedforward and recurrent networks, convolutional models, and standard transformers. While baseline models perform well under interpolation, they exhibit a pronounced generalization gap when evaluated on fuels not included in the training set. The proposed model consistently improves extrapolative accuracy and stability, yielding the strongest performance on unseen fuel configurations. These results indicate that a lightweight physics structure embedded within attention mechanisms can substantially improve robustness, enabling more reliable surrogate predictions to accelerate the design of nuclear fuel irradiation experiments.

Fuel qualification↗
DOE OSTI2017

Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon

We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from O ($N$ $^{2}_{ϵ}$) to O ( N ϵ ) when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn–Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in O ($N$ $^{3}_{ϵ}$) operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the resulting ACE-ISDF method significantly reduces the computational cost associated with the exchange operator by nearly 2 orders of magnitude compared to existing approaches for a large silicon system with 1000 atoms. We demonstrate that the ACE-ISDF method can produce accurate energies and forces for insulating and metallic systems and that it is possible to obtain converged hybrid functional calculation results for a 1000-atom bulk silicon within 10 min on 2000 computational cores. We also show that ACE-ISDF can scale to 8192 computational cores for a 4096-atom bulk silicon system. We use the ACE-ISDF method to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure. Here, we find that that the computed energy gap from the HSE06 functional is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting

We investigate the use of interpolative separable density fitting (ISDF) as a means to reduce the memory bottleneck in auxiliary field quantum Monte Carlo (AFQMC) simulations of real materials in Gaussian basis sets. Here, we find that ISDF can reduce the memory scaling of AFQMC simulations from O(M 4 ) to O(M 2 ) . We test these developments by computing the structural properties of carbon in the diamond phase, comparing to results from existing computational methods and experiment. (LLNL-JRNL-759024)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Interpolated Wave Functions for Nonadiabatic Simulations with the Fixed-Node Quantum Monte Carlo Method. In: Recent Progress in Quantum Monte Carlo, Chapter 3

Simulating nonadiabatic effects with many-body wave function approaches is an open field with many challenges. Recent interest has been driven by new algorithmic developments and improved theoretical understanding of properties unique to electron-ion wave functions. Fixed-node diffusion Monte Caro is one technique that has shown promising results for simulating electron-ion systems. In particular, we focus on the CH molecule for which previous results suggested a relatively significant contribution to the energy from nonadiabatic effects. We propose a new wave function ansatz for diatomic systems which involves interpolating the determinant coefficients calculated from configuration interaction methods. The calculated nonadiabatic contribution to the energy in the CH molecule is reduced compared to our previous results, but still remains the largest among the molecules under consideration.

Tubman, Norm M.↗
DOE OSTI2016

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

MorphOT: transport-based interpolation between EM maps with UCSF ChimeraX

Cryogenic electron microscopy (cryo-EM) offers the unique potential to capture conformational heterogeneity, by solving multiple three-dimensional classes that co-exist within a single cryo-EM image dataset. To investigate the extent and implications of such heterogeneity, we propose to use an optimal-transport-based metric to interpolate barycenters between EM maps and produce morphing trajectories.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Multiparticle interpolating operators in quantum field theories with cubic symmetry

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multiparticle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and nonzero spin.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

b ¯ b ¯ u d and b ¯ b ¯ u s tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators

We study the b ¯ b ¯ u d tetraquark with quantum numbers I ( J P ) = 0 ( 1 + ) as well as the b ¯ b ¯ u s tetraquark with quantum numbers J P = 1 + using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, − 100 ± 10 − 51 + 36 MeV for b ¯ b ¯ u d and − 30 ± 3 − 31 + 11 MeV for b ¯ b ¯ u s , are consistent with other recent lattice-QCD predictions. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2021

Combined Dimensional and Topology Optimization of Interior Permanent Magnet Synchronous Machine Rotors Using a Permanent Magnet Function Interpolation Method

This paper presents a magneto-structural combined dimensional and topology optimization technique for interior permanent magnet synchronous machine (IPMSM) rotors. Dimensional changes to the permanent magnet (PM) 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. A density based Solid Isotropic with Material 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. Three examples are presented to demonstrate the technique: two flat bar IPMSM and one V-shaped IPMSM.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Optimizing Error-Bounded Lossy Compression for Scientific Data by Dynamic Spline Interpolation

Today's scientific simulations are producing vast volumes of data that cannot be stored and transferred efficiently because of limited storage capacity, parallel I/O bandwidth, and network bandwidth. The situation is getting worse over time because of the ever-increasing gap between relatively slow data transfer speed and fast-growing computation power in modern supercomputers. Error-bounded lossy compression is becoming one of the most critical techniques for resolving the big scientific data issue, in that it can significantly reduce the scientific data volume while guaranteeing that the reconstructed data is valid for users because of its compression-error-bounding feature. In this paper, we present a novel error-bounded lossy compressor based on a state-of-the-art prediction-based compression framework. Our solution exhibits substantially better compression quality than all of the existing error-bounded lossy compressors, with comparable compression speed. Specifically, our contribution is threefold. (1) We provide an in-depth analysis of why the best-existing prediction-based lossy compressor can only minimally improve the compression quality. (2) We propose a dynamic spline interpolation approach with a series of optimization strategies that can significantly improve the data prediction accuracy, substantially improving the compression quality in turn. (3) We perform a thorough evaluation using six real-world scientific simulation datasets across different science domains to evaluate our solution vs. all other related works. Experiments show that the compression ratio of our solution is higher than that of the second-best lossy compressor by 20%similar to 460% with the same error bound in most of the cases.

Zhao, Kai↗
DOE OSTI2016

Contour interpolated radial basis functions with spline boundary correction for fast 3D reconstruction of the human articular cartilage from MR images

Purpose: The aim of this work is to demonstrate a new image processing technique that can provide a “near real-time” 3D reconstruction of the articular cartilage of the human knee from MR images which is user friendly. This would serve as a point-of-care 3D visualization tool which would benefit a consultant radiologist in the visualization of the human articular cartilage. Methods: The authors introduce a novel fusion of an adaptation of the contour method known as “contour interpolation (CI)” with radial basis functions (RBFs) which they describe as “CI-RBFs.” The authors also present a spline boundary correction which further enhances volume estimation of the method. A subject cohort consisting of 17 right nonpathological knees (ten female and seven male) is assessed to validate the quality of the proposed method. The authors demonstrate how the CI-RBF method dramatically reduces the number of data points required for fitting an implicit surface to the entire cartilage, thus, significantly improving the speed of reconstruction over the comparable RBF reconstruction method of Carr. The authors compare the CI-RBF method volume estimation to a typical commercial package (3D DOCTOR), Carr’s RBF method, and a benchmark manual method for the reconstruction of the femoral, tibial, and patellar cartilages. Results: The authors demonstrate how the CI-RBF method significantly reduces the number of data points (p-value < 0.0001) required for fitting an implicit surface to the cartilage, by 48%, 31%, and 44% for the patellar, tibial, and femoral cartilages, respectively. Thus, significantly improving the speed of reconstruction (p-value < 0.0001) by 39%, 40%, and 44% for the patellar, tibial, and femoral cartilages over the comparable RBF model of Carr providing a near real-time reconstruction of 6.49, 8.88, and 9.43 min for the patellar, tibial, and femoral cartilages, respectively. In addition, it is demonstrated how the CI-RBF method matches the volume estimation of a typical commercial package (3D DOCTOR), Carr’s RBF method, and a benchmark manual method for the reconstruction of the femoral, tibial, and patellar cartilages. Furthermore, the performance of the segmentation method used for the extraction of the femoral, tibial, and patellar cartilages is assessed with a Dice similarity coefficient, sensitivity, and specificity measure providing high agreement to manual segmentation. Conclusions: The CI-RBF method provides a fast, accurate, and robust 3D model reconstruction that matches Carr’s RBF method, 3D DOCTOR, and a manual benchmark method in accuracy and significantly improves upon Carr’s RBF method in data requirement and computational speed. In addition, the visualization tool has been designed to quickly segment MR images requiring only four mouse clicks per MR image slice.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Interpolation-Based Composite Derivative-Free Optimization (IBCDFO)

IBCDFO is a library of interpolation-based optimization methods for composite derivative-free optimization. These methods are applicable when optimizing a function that depends on multiple outputs from a blackbox experiment/simulation for which derivatives with respect to the decision variables are not available. The methods include POUNDerS and GOOMBAH.

Wild, Stefan [Lawrence Berkeley National Laborator↗
DOE OSTI2016

LIP: The Livermore Interpolation Package, Version 1.6

This report describes LIP, the Livermore Interpolation Package. LIP was totally rewritten from the package described in [1]. In particular, the independent variables are now referred to as x and y, since it is a general-purpose package that need not be restricted to equation of state data, which uses variables ρ (density) and T (temperature).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Subcontract B629176: Algebraic Multigrid with Optimal Interpolation (Final Report)

Progress has been made in several of the proposed areas of research, as summarized below: Compatible Relaxation and Optimal Interpolation and Bootstrap Algebraic Multigrid and non-Galerkin AMG for the Dirac equations. Our preliminary findings are promising and suggest that these techniques should lead to efficient and robust solvers for various discretizations of the Dirac PDE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Interpolation of V-Gamma Map Failure Data for Use with LAPS

This document outlines the approach used for interpolation of a dataset provided by the Jet Propulsion Laboratory (JPL) which contains failure predictions of the Mars 2020 entry vehicle (EV). JPL used Navier-Stokes simulations to predict the failure altitude of the EV, along with a corresponding velocity and flight path angle at failure. These simulations were executed for several initial trajectory points in the entry envelope (the V-Gamma map).

42 ENGINEERING↗