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DOE OSTI2024

A General Framework for Error-controlled Unstructured Scientific Data Compression

Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression ratios. We present a multi-component, error-bounded compression framework designed to enhance the compression of floating-point unstructured mesh data, which is common in scientific applications. Our approach involves interpolating mesh data onto a rectilinear grid and then separately compressing the grid interpolation and the interpolation residuals. This method is general, independent of mesh types and typologies, and can be seamlessly integrated with existing lossy compressors for improved performance. We evaluated our framework across twelve variables from two synthetic datasets and two real-world simulation datasets. The results indicate that the multi-component framework consistently outperforms state-of-the-art lossy compressors on unstructured data, achieving, on average, a 2.3 − 3.5× improvement in compression ratios, with error bounds ranging from 1 × 10 the −6 to 1×10−2. We further investigate impact of hyperparameters, such as grid spacing and error allocation, to deliver optimal compression ratios in diverse datasets.

Gong, Qian↗

DOE OSTI2025

Analog In-Memory Computing for the Synthetic Aperture Radar Polar Format Algorithm

As the utility of synthetic aperture radar (SAR) systems increases in autonomous vehicles, satellites, and other power- and space-constrained edge applications, there is a growing need for processors that can form SAR images at low power. In recent years, analog in-memory compute (AIMC) has shown immense promise for accelerating neural networks and other matrix-vector multiplication (MVM) heavy workloads at the edge. Here, in this work, we examine how the polar format algorithm (PFA), a popular SAR image formation algorithm, can be mapped to these AIMC systems. The PFA maps readily onto analog MVMs because it primarily consists of two linear operations: interpolation of frequency-domain data to a Cartesian grid, followed by a 2-D Fourier transform. This work presents two approaches to map the interpolation operation onto MVMs in analog hardware: a chirp transform and a modified form of sinc interpolation. These mappings introduce algorithmic errors, and their effect on the quality of SAR image formation is examined, both quantitatively and qualitatively. In addition, the impact of errors introduced by the analog hardware is explored to determine which approach is optimal under varying assumptions about the underlying analog memory devices and circuits.

Analog computing↗

DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Bias Corrected NOAA HRRR Wind Resource Data for Grid Integration Applications

To address the need for regularly updated wind resource data, NREL has processed the High-Resolution Rapid Refresh (HRRR) outputs for use in grid integration modeling. The HRRR is an hourly-updated operational forecast product produced by the National Oceanic and Atmospheric Administration (NOAA) (Dowell et al., 2022). Several barriers have prevented the HRRR's widespread proliferation in the wind energy industry: missing timesteps (prior to 2019), challenging file format for wind energy analysis, limited vertical height resolution, and negative bias versus legacy WIND Toolkit data (2007-2013). NREL has applied re-gridding, interpolation, and bias-correction to the native HRRR data to overcome these limitations. This results in the now-publicly-available bias corrected and interpolated HRRR (BC-HRRR) dataset for weather years 2015 to 2023. Bias correction is necessary for wind resource consistency across weather years to be used simultaneously in planning-focused grid integration studies alongside the original WIND Toolkit data. We show that quantile mapping with the WIND Toolkit as a historical baseline is an effective method for bias correcting the interpolated HRRR data: the BC-HRRR has reduced mean bias versus comparable gridded wind resource datasets (+0.12 m/s versus Vortex) and has very low mean bias versus ground measurement stations (+0.01 m/s) (Buster et al., 2024). BC-HRRR's consistency with the legacy WIND Toolkit allows NREL to extend grid integration analysis to 15+ weather years of wind data with low-overhead extensibility to future years as they are made available by NOAA. As with historical datasets like the WIND Toolkit, BC-HRRR is intended for use in grid integration modeling (e.g., capacity expansion, production cost, and resource adequacy modeling) both independently and alongside the legacy WIND Toolkit.

Array↗

DOE OSTI2026

A Centralized AI Lakehouse Framework for Brain Tumor MRI Classification and Segmentation, University KPI Forecasting, and Water Potability Prediction

In many university and healthcare projects, models are built for very different data types such as tables, institutional time series, and medical images, but they are deployed as separate applications. In this work, that separation made testing and maintenance difficult because each module had its own pipeline and runtime requirements. This paper presents an integrated AI lakehouse-style implementation that runs three model pipelines inside one containerized backend. For medical imaging, we used MRI datasets from IEEE DataPort: a four-class classification set with 7012 images (5708 train/1304 test) and a segmentation set with 3063 image–mask pairs. The classification model (ResNet50 transfer learning) is evaluated using a proper train–validation–test protocol across multiple splits (80/10/10, 70/10/20, 60/10/30, and 10/30/60), achieving a test accuracy of 99.00% under the standard 80/10/10 split. Additionally, a patient-level evaluation is conducted using an external glioma dataset to provide a more realistic assessment without data leakage. The segmentation model (DeepLabV3-ResNet50) achieved 83.09% validation mIoU and 88.79% Dice score. For university KPI forecasting, we used annual IPEDS and NSF HERD data from 2010 to 2023 for three universities (BSU, EOU, and UAB). To examine the effect of preprocessing on forecasting performance, two case studies are conducted. In the first case, linear interpolation is applied to generate semester-level data. In the second case, the original annual data is used directly without interpolation. Random Forest regression and ARIMA models are evaluated using MAE, RMSE, MAPE, and R 2 . The results showed that interpolation improved apparent forecasting performance due to smoothing, while evaluation on the original annual data provided a more realistic assessment of model behavior. To further validate the framework on a larger dataset, an additional case study is conducted using a student dropout dataset. For water potability, we trained and compared multiple tabular classifiers on a large dataset (1,048,575 samples). A Random Forest model (100 trees, max depth 10) achieved 85.86% test accuracy and high recall for unsafe samples (0.8447). All modules are served via FastAPI and deployed together using Docker, with workflow automation routing requests to the correct endpoint. System-level benchmarking indicates that the backend maintains stable throughput and latency under concurrent requests.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Exact finite elements for conduction and convection

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Thornton, E. A.↗

NASA NTRS1981

Exact finite elements for conduction and convection

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Thornton, E. A.↗

NASA NTRS1983

Three-dimensional algebraic grid generation

One of the major approaches to numerical grid generation is the explicit algebraic expression of a physical grid as a function of a uniform grid in a rectangular computational coordinate system. The algebraic methods are based on mathematical interpolation, and the primary advantages are speed and directness. The relation between interpolation and grid generation is described. For three-dimensional grid generation, transfinite interpolation using the coordinate control processes developed in the multisurface method and two-boundary technique are advocated. Grid singularities encountered in three dimensions are discussed, and the exploration of multiple overlapping grids is proposed. Some aspects of interactive algebraic grid computation in three dimensions are discussed.

Smith, R. E.↗

NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗

NASA NTRS1985

Mean Winds and Tides over Urbana, Illinois During November 16-22, 1981

The Urbana Meteor Radar uses a high power pulse transmitter to achieve high echo rates, and an interferometer to spatially locate the individual echoes. The irregularly spaced observations of range, radial velocity, and direction cosines are reduced to a rectangular grid, evenly spaced in time and height, of estimates of the zonal and meridional wind. This is accomplished using the method of GROVES whereby a constant horizontal wind is fitted, using least squares, to all echoes occurring within a fixed time/height interval. This interpolation region is then stepped in time and height. the size of the interpolation region is 2 hours by 5 km, the time step is approximately 11 minutes, and the height step is 2 km. The filtering of high temporal and spatial frequencies is somewhat reduced by weighting the echoes according to their distance from the center of the interpolation box.

Tetenbaum, D.↗

NASA NTRS1986

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗

NASA NTRS1986

A data base and analysis program for shuttle main engine dynamic pressure measurements

A dynamic pressure data base management system is described for measurements obtained from space shuttle main engine (SSME) hot firing tests. The data were provided in terms of engine power level and rms pressure time histories, and power spectra of the dynamic pressure measurements at selected times during each test. Test measurements and engine locations are defined along with a discussion of data acquisition and reduction procedures. A description of the data base management analysis system is provided and subroutines developed for obtaining selected measurement means, variances, ranges and other statistics of interest are discussed. A summary of pressure spectra obtained at SSME rated power level is provided for reference. Application of the singular value decomposition technique to spectrum interpolation is discussed and isoplots of interpolated spectra are presented to indicate measurement trends with engine power level. Program listings of the data base management and spectrum interpolation software are given. Appendices are included to document all data base measurements.

Coffin, T.↗

NASA NTRS1985

Modified cubic convolution resampling for Landsat

An overview is given of Landsat Thematic Mapper resampling technique, including a modification of the well-known cubic convolution interpolator (nearest neighbor interpolation) used to provide geometric correction for TM data. Post launch study has shown that the modified cubic convolution interpolator can selectively enhance or suppress frequency bands in the output image. This selectivity is demonstrated on TM Band 3 imagery.

Prakash, A.↗

NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

Efforts in transferring computational work from the LRC computer to the IRIS Graphics Workstation at MSU are reported and the computation of a conservative solution of a simple hyperbolic equation on an overlapping grid is discussed. Several conclusions concerning computations on overlapping grids are apparent. Problems only occur when there is a major difference in grid spacing on the individual component grids. In the case of hyperbolic equations, it is necessary that both interpolation and extrapolation be applied at the grid boundaries. When interpolated values are used at outflow boundary points, excessive oscillations in the numerical solution may be the result. The same conclusions would be valid for more complicated systems of hyperbolic equations such as the Euler equations for inviscid flow. Some of the solution values would be extrapolated at the overlap boundary, the exact number depending on the number of characteristics pointing out of the overlap region. It is also possible that similar boundary conditions may be needed for some parabolic equations such as high Reynolds number viscous flow equations. Efforts were also expended on the development of three-dimensional conservative interpolation procedures. Finally, the investigation of grid smoothing procedures were initiated during this reporting period. It was decided that the first grid smoothing algorithms will be based on the concepts of variational grid generation.

Mastin, C. W.↗

NASA NTRS1987

Nighttime atmospheric stability changes and their effects on the temporal intensity of a mesoscale convective complex

A method of interpolating atmospheric soundings while reducing the errors associated with simple time interpolation was developed. The purpose of this was to provide a means to determine atmospheric stability at times between standard soundings and to relate changes in stability to intensity changes in an MCC. Four MCC cases were chosen for study with this method with four stability indices being included. The discussion centers on three aspects for each stability parameter examined: the stability field in the vicinity of the storm and its changes in structure and magnitude during the lifetime of the storm, the average stability within the storm boundary as a function of time and its relation to storm intensity, and the apparent flux of stability parameter into the storm as a consequence of low-level storm relative flow. It was found that the results differed among the four stability parameters, sometimes in a conflicting fashion. Thus, an interpolation of how the storm intensity is related to the changing environmental stability depends upon the particular index utilized. Some explanation for this problem is offered.

Hovis, Jeffrey S.↗

NASA NTRS1987

A finite element computational method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.

Kim, Sang-Wook↗

NASA NTRS1988

Application Of Prony's Method To Data On Viscoelasticity

Prony coefficients found by computer program, without trial and error. Computational method and computer program developed to exploit full potential of Prony's interpolation method in analysis of experimental data on relaxation modules of viscoelastic material. Prony interpolation curve chosen to give least-squares best fit to "B-spline" interpolation of experimental data.

Rodriguez, Pedro I.↗

NASA NTRS1988

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.

Kim, Sang-Wook↗