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Results for “least-squares analysis”

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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50 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Efficient data-driven regression for reduced-order modeling of spatial pattern formation

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.

Data-driven modeling↗
DOE OSTI2021

Rapid quantitative analysis of trace elements in plutonium alloys using a handheld laser-induced breakdown spectroscopy (LIBS) device coupled with chemometrics and machine learning

Here, we present the first reported quantification of trace elements in plutonium via a portable laser-induced breakdown spectroscopy (LIBS) device and demonstrate the use of chemometric analysis to enhance the handheld device's sensitivity and precision. Quantification of trace elements such as iron and nickel in plutonium metal via LIBS is a challenging problem due to the complex nature of the plutonium optical emission spectra. While rapid analysis of plutonium alloys has been demonstrated using portable LIBS devices, such as the SciAps Z300, their detection limits for trace elements are severely constrained by their achievable pulse power and length, light collection optics, and detectors. In this paper, analytical methods are evaluated as a means to circumvent the detection constraints. Three chemometric methods often used in analytical spectroscopy are evaluated; principal component regression, partial least-squares regression, and artificial neural networks. These models are evaluated based on goodness-of-fit metrics, root mean-squared error, and their achievable limits of detection (LoDs). Partial least squares proved superior for determining content of iron and nickel in plutonium metal, yielding LoDs of 15 and 20 ppm, respectively. These results of identifying the undesirable trace elements in plutonium components are critical for applications such as fabricating radioisotope thermoelectric generators or nuclear fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Proper orthogonal descriptors for efficient and accurate interatomic potentials

Here, we present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials are functions of atom positions and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials into a set of proper orthogonal descriptors (PODs). Because of the rapid convergence of the proper orthogonal decomposition, relevant snapshots can be sampled exhaustively to represent the atomic neighborhood environment accurately with a small number of descriptors. The proper orthogonal descriptors are used to develop interatomic potentials by using a linear expansion of the descriptors and determining the expansion coefficients from a weighted least-squares regression against a density functional theory (DFT) training set. We present a comprehensive evaluation of the POD potentials on previously published DFT data sets comprising Li, Mo, Cu, Ni, Si, Ge, and Ta elements. The data sets represent a diverse pool of metals, transition metals, and semiconductors. The accuracy of the POD potentials are comparable to that of state-of-the-art machine learning potentials such as the spectral neighbor analysis potential (SNAP) and the atomic cluster expansion (ACE).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bayesian model averaging for analysis of lattice field theory results

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be considered for the same lattice data. Model averaging, which amounts to a probability-weighted average over all model variations, can incorporate systematic errors associated with model choice without being overly conservative. We discuss the framework of model averaging from the perspective of Bayesian statistics, and give useful formulae and approximations for the particular case of least-squares fitting, commonly used in modeling lattice results. In addition, we frame the common problem of data subset selection (e.g. choice of minimum and maximum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a straightforward alternative to manual selection of fit ranges. Numerical examples involving both mock and real lattice data are given.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Background optimization of powder electron diffraction for implementation of the e-PDF technique and study of the local structure of iron oxide nanocrystals

The local structural characterization of iron oxide nanoparticles is explored using a total scattering analysis method known as pair distribution function (PDF) (also known as reduced density function) analysis. The PDF profiles are derived from background-corrected powder electron diffraction patterns (the e-PDF technique). Due to the strong Coulombic interaction between the electron beam and the sample, electron diffraction generally leads to multiple scattering, causing redistribution of intensities towards higher scattering angles and an increased background in the diffraction profile. In addition to this, the electron–specimen interaction gives rise to an undesirable inelastic scattering signal that contributes primarily to the background. The present work demonstrates the efficacy of a pre-treatment of the underlying complex background function, which is a combination of both incoherent multiple and inelastic scatterings that cannot be identical for different electron beam energies. Therefore, two different background subtraction approaches are proposed for the electron diffraction patterns acquired at 80 kV and 300 kV beam energies. From the least-square refinement (small-box modelling), both approaches are found to be very promising, leading to a successful implementation of the e-PDF technique to study the local structure of the considered nanomaterial.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Rapid monitoring of fermentations: a feasibility study on biological 2,3-butanediol production

2,3-butanediol (2,3-BDO) is an economically important platform chemical that can be produced by the fermentation of sugars using an engineered strain of Zymomonas mobilis . These fermentations require continuous monitoring and modification of fermentation conditions to maximize 2,3-BDO yields and minimize the production of the undesired coproducts glycerol and acetoin. Because of the time required for sampling and off-line chromatographic measurement of fermentation samples, the ability of fermentation scientists to modify fermentation conditions in a timely manner is limited. The goal of this study was to test if near-infrared spectroscopy (NIRS) along with multivariate statistics could reduce the time needed for this analysis and enable real-time monitoring and control of the fermentation. In this work we developed partial least squares (PLS) calibration models to predict the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol in fermentations via NIRS using two different spectrometers and two different spectroscopy modalities. We first evaluated the feasibility of rapid NIRS monitoring through experiments where we measured the signals from each analyte of interest and built NIRS-based PLS models using spectra from synthetic samples containing uncorrelated concentrations of these analytes. All analytes showed unique spectral signatures, and this initial modeling showed that all analytes could be detected simultaneously. We then began work with samples from laboratory fermentation experiments and tested the feasibility of regression model development across two spectral collection modalities (at-line and on-line) and two instruments: a laboratory-grade instrument and a low-cost instrument with a more limited spectral range. All modalities showed promise in the ability to monitor Z. mobilis fermentations of glucose and xylose to 2,3-BDO. The low-cost instrument displayed a lower signal-to-noise ratio than the laboratory-grade instrument, which led to comparatively lower performance overall, but still provided sufficient accuracy to monitor fermentation trends. While the ease of use of on-line monitoring systems was favored as compared to at-line systems due to the lack of sampling required and potential for automated process control, we observed some decrease in performance due to the additional complexity of the sample matrix. We have demonstrated that NIRS combined with multivariate analysis can be used for at-line and on-line monitoring of the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol during Z. mobilis fermentations. The decrease in signal-to-noise ratio when using a low-cost spectrometer led to greater prediction error than the laboratory-grade spectrometer for at-line monitoring. The on-line monitoring modality showed great promise for real time process control via NIRS.

09 BIOMASS FUELS↗
DOE OSTI2024

G2Aero Database of Airfoils - Curated Airfoils

This dataset contains a curated set of 19,164 airfoil shapes from various applications and the data-driven design space of separable shape tensors (PGA space), which can be used as a parameter space for machine-learning applications focused on airfoil shapes. We constructed the airfoil dataset in two main stages. First, we identified 13 baseline airfoils from the NREL 5MW and IEA 15MW reference wind turbines. We reparameterized these shapes using least-squares fits of 8-order CST parametrizations, which involve 18 coefficients. By uniformly perturbing all 18 CST coefficients by +/-20% around each baseline airfoil, we generated 1,000 unique airfoils. Each airfoil was sampled with 1,001 shape landmarks whose x-coordinates followed a cosine distribution along the chord. This process resulted in a total of 13,000 airfoil shapes, each with 1,001 landmarks. In the second phase, we gathered additional airfoils from the extensive BigFoil database, which consolidates data from sources such as the University of Illinois Urbana-Champaign (UIUC) airfoil database, the JavaFoil database, the NACA-TR-824 database, and others. We undertook a thorough pre-processing step to filter out shapes with sparse, noisy, or incomplete data. We also removed airfoils with sharp leading edge and those exceeding our threshold for trailing edge thickness. Additionally, we thinned out the collection of NACA airfoils-- parametric sweeps of NACA airfoils with increasing thickness and camber present in BigFoil database-- by selecting every fourth step in the parameter sweeps. Finally, we regularized the airfoils by reparametrizing them with an 8-order CST parametrization (with 1,001 shape landmarks with x coordinated following cosine distribution along the chord) and removing airfoils with high reconstruction errors. This data pre-processing resulted in a set of 6,164 airfoils. In total, our curated airfoil dataset comprises 19,164 airfoils, each with 1,001 landmarks, and is stored in the curated_airfoils.npz file. Using this curated airfoil dataset, we utilized the separable shape tensors framework to develop a data-driven parameterization of airfoils based on principal geodesic analysis (PGA) of separable shape tensors. This PGA space is provided in PGAspace.npz file.

airfoils↗
DOE OSTI2023

Simultaneous determination of electrical conductivity and thickness of nonmagnetic metallic foils using two-sided multifrequency eddy current techniques

Here, in this paper, we describe a simple method for performing multifrequency eddy current characterization of free-standing uniform-thickness metallic foils using a forked inductive coil arrangement. The method involves measuring the mutual inductance between two coils when a foil is present between the coils, and when it is not present; the ratio of these mutual inductances is compared with an analytical solution, and foil conductivity, thickness, and sheet resistance are simultaneously estimated using numerical inversion and least-squares fitting. This method was used to characterize 34 non-ferrous metallic samples with thicknesses between 50 and 640 μm and with conductivities between 0.8 × 10 7 and 5.8 × 10 7 S/m. The estimated thicknesses from eddy current characterization agreed well with those measured using confocal optical techniques; the two approaches agreed to within 1 μm for samples that were thinner than 200 μm, and to within 0.5% for samples that had a thickness of 200 μm or greater. The estimated conductivities from eddy current characterization were in close agreement with expected values, given knowledge of the materials used. A particular strength of this approach is that the instrumentation needed is broadly available in research and development laboratories and the associated fixturing is easy to manufacture and assemble. A calibration procedure is described that can be used to reduce errors from geometric uncertainties. This calibration requires a sample that has only a known conductivity or thickness; both do not need to be known. The method described herein is likely extensible to conductivities and thickness well outside the ranges measured as part of this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Leveraging Multiple Raman Excitation Wavelength Systems for Process Monitoring of Nuclear Waste Streams

Processing nuclear waste from sites such as Hanford is a significant environmental cleanup need while being a significant logistical challenge. Integration of process monitoring tools, that can provide in situ and real-time feedback about the process, can significantly alleviate needs to collect grab samples for process control and product characterization. Raman spectroscopy paired with chemometric analysis is one process monitoring tool that can provide chemical composition information on a large number of chemical targets in nuclear waste streams. However, methods to improve limits of detection as well as drop uncertainty in quantification are needed. Optimizing instrument specifications can achieve this, here this is demonstrated by comparing limits of detection for key analytes when using Raman systems with 671 nm, 532 nm, and 405 nm excitation wavelengths. Generally, limits of detection decease (allowing the measurement of lower salt concentrations) with decreasing wavelength. Similarly, data collection times and averaging were optimized. Finally, multiple chemometric modeling approaches were leveraged, including multiblock methods that combined data from all three Raman systems to simultaneously quantify targets with improved sensitivity.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Tracking seasonal variability in plant traits from spaceborne PRISMA and NEON AOP across forest types and ecoregions

Plant traits serve as critical indicators of how plants adapt to environmental changes and influence ecosystem functions. While airborne hyperspectral remote sensing effectively maps plant traits through detailed reflectance properties, it is limited by cost and scale, making large-scale and temporal studies challenging. The recently launched spaceborne hyperspectral imager, PRecursore IperSpettrale della Missione Applicativa (PRISMA), offers frequent, large scale and high-fidelity observations on a spatial resolution of 30 m and a revisit time of around 29 days, making it suitable for large-scale seasonal trait mapping. However, their potential remains largely unexplored. This study developed a multi-stage framework by leveraging the PRISMA spaceborne hyperspectral data and National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP) hyperspectral data to investigate the seasonal dynamics of four key plant traits — chlorophyll content, carotenoid content, equivalent water thickness, and nitrogen content — across eleven NEON sites representing diverse forest types and ecoregions in the contiguous U.S. Our results demonstrated that PRISMA hyperspectral data can reliably track seasonal variability in plant traits, achieving overall R 2 values ranging from 0.78 to 0.88 and normalized root mean square error (NRMSE) values ranging from 5.4% to 8.4% for the four traits. Seasonal patterns revealed bell-shaped trajectories for chlorophyll and carotenoids, while equivalent water thickness decreased steadily across most sites, driven by structural changes during leaf maturation and senescence. Nitrogen content exhibited less pronounced seasonal variation but followed expected nutrient resorption patterns. Analysis of environmental drivers showed that seasonal variability is primarily controlled by solar radiation and day length in northern sites, vapor pressure in semi-arid regions, and temperature in mid-southeastern sites. Spatial variability, meanwhile, was primarily driven by soil properties, particularly during the peak growing season. However, the influence of soil variables slightly declines toward the end of the season at several sites, as climatic factors become more prominent. This study highlights the capability of PRISMA, and potentially other similar spaceborne hyperspectral data for large-scale, time-series plant trait mapping and provides valuable insights into the interactions between plant traits and environmental factors. In conclusion, these findings contribute to advancing our understanding of plant functional ecology and improving predictions of ecosystem responses to environmental changes.

Environmental drivers↗
DOE OSTI2021

Parameter dependencies of the experimental nitrogen concentration required for detachment on ASDEX Upgrade and JET

While current tokamak experiments are beginning to use real-time feedback control systems to manage the plasma exhaust, future tokamaks still require validation of theoretical models used to predict the threshold impurity concentration required to sufficiently reduce the power and particle fluxes to the divertor. This work exploits new spectroscopic measurements of the divertor nitrogen concentration, c n , in partially detached N 2 -seeded H-mode plasmas on ASDEX Upgrade (AUG) and JET with the ITER-Like Wall (JET-ILW) to test the parameter dependencies of the power flowing to the outer divertor, P div,outer , and the separatrix electron density, n e.sep . A least-squares regression of the AUG measurements demonstrates that the threshold c n required for detachment scales as $c_n∝P^{1.19±0.32}_{div,outer}n^{-2.77±0.36}_{e,sep}$. This scaling of n e,sep is also consistent with the measurements from JET which, at constant P div,outer , show $c_n∝n^{-2.43±0.27}_{e,sep}$. The dependencies of P div,outer and n e.sep is demonstrated over at least a factor of two change in both parameters and indicates a stronger dependence on n e.sep in comparison to the Lengyel model, which could be due to the assumption in this model that the heat flux channel width is independent of density. This first assessment of detachment scaling with impurity seeding highlights the need for further analysis of the systematic uncertainties of the measurement and more consistent scenarios from more tokamaks to investigate the machine size scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Comparing Sensor Fusion and Multimodal Chemometric Models for Monitoring U(VI) in Complex Environments Representative of Irradiated Nuclear Fuel

Optical sensors and chemometric models were leveraged for the quantification of uranium(VI) (0–100 μg mL –1 ), europium (0–150 μg mL –1 ), samarium (0–250 μg mL –1 ), praseodymium (0–350 μg mL –1 ), neodymium (0–1000 μg mL –1 ), and HNO 3 (2–4 M) with varying corrosion product (iron, nickel, and chromium) levels using laser fluorescence, Raman scattering, and ultraviolet–visible–near-infrared absorption spectra. In this paper, an efficient approach to developing and evaluating tens of thousands of partial least-squares regression (PLSR) models, built from fused optical spectra or multimodal acquisitions, is discussed. Each PLSR model was optimized with unique preprocessing combinations, and features were selected using genetic algorithm filters. The 7-factor D-optimal design training set contained just 55 samples to minimize the number of samples. The performance of PLSR models was evaluated by using an automated latent variable selection script. PLS1 regression models tailored to each species outperformed a global PLS2 model. PLS1 models built using fused spectra data and a multimodal (i.e., analyzed separately) approach yielded similar information, resulting in percent root-mean-square error of prediction values of 0.9–5.7% for the seven factors. Further, the optical techniques and data processing strategies established in this study allow for the direct analysis of numerous species without measuring luminescence lifetimes or relying on a standard addition approach, making it optimal for near-real-time, in situ measurements. Nuclear reactor modeling helped bound training set conditions and identified elemental ratios of lanthanide fission products to characterize the burnup of irradiated nuclear fuel. Leveraging fluorescence, spectrophotometry, experimental design, and chemometrics can enable the remote quantification and characterization of complex systems with numerous species, monitor system performance, help identify the source of materials, and enable rapid high-throughput experiments in a variety of industrial processes and fundamental studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Estimating and Calibrating DER Model Parameters Using Levenberg–Marquardt Algorithm in Renewable Rich Power Grid

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power–voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg–Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss–Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed by the numerical calculation of the Jacobian are tackled using a quasi-Newton root-finding approach. The proposed method is validated on a real feeder model in the northeastern part of the United States. The feeder is modeled in OpenDSS and the measurements thus obtained are fed to the DER_A model for calibration. The simulation results indicate that our approach is able to successfully calibrate the relevant model parameters quickly and with high accuracy, with a total sum of square error of 3.57 × 10 –7 .

29 ENERGY PLANNING, POLICY, AND ECONOMY↗