Search NASA⌕ Search

SEARCH · Search NASA

Results for “least-squares”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

4D beam matrix reconstruction in particle accelerators

Transverse beam parameters in particle accelerators are commonly described using the Twiss parameters, which are experimentally accessible yet inherently limited because they neglect correlations between different transverse coordinates. Such correlations frequently arise from uncompensated cathode magnetic fields or misaligned focusing quadrupoles, affecting beam quality and accelerator performance. To address this limitation, we propose and validate a novel diagnostic method for the complete four-dimensional (4D) transverse beam matrix. Our method involves passing the beam through a beamline comprising both conventional and skew quadrupole magnets, followed by downstream measurements of the resulting two-dimensional (2D) beam profiles. These measurements represent distinct 2D projections of the underlying 4D transverse phase–space distribution. By systematically varying quadrupole strengths, multiple independent projections of the beam phase space are obtained. We reconstruct the original 4D beam matrix from these measured projections using an optimization-based least-square fit, providing fast and robust reconstruction regardless of the specific beamline configuration. Through extensive numerical simulations and realistic particle-tracking studies, we demonstrate the diagnostic’s accuracy, robustness, and capability to achieve reconstruction uncertainties smaller than measurement errors, particularly when employing sufficient numbers of quadrupole scans. This method presents a powerful and flexible approach for comprehensive beam characterization and accelerator tuning.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Inferring effective electrostatic interaction of charge-stabilized colloids from scattering using deep learning

In this article, an innovative strategy is presented that incorporates deep auto-encoder networks into a least-squares fitting framework to address the potential inversion problem in small-angle scattering. To evaluate the performance of the proposed approach, a detailed case study focusing on charged colloidal suspensions was carried out. The results clearly indicate that a deep learning solution offers a reliable and quantitative method for studying molecular interactions. The approach surpasses existing deterministic approaches with respect to both numerical accuracy and computational efficiency. Overall, this work demonstrates the potential of deep learning techniques in tackling complex problems in soft-matter structures and beyond.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗
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 OSTI2024

How Much Reserve Fuel: Quantifying the Maximal Energy Cost of System Disturbances

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances, compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear, time-invariant system. We compare the nominal energy required to achieve this task in the disturbance-free system to the worst-case energy over all feasible disturbances. Solving for the worst-case energy over all disturbances first leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of energies is accomplished using additive and multiplicative metrics, for which we derive bounds. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the distance of the initial condition from the origin and the task completion time.

koopman operator, resilience↗
DOE OSTI2024

Statistical Behavior of Low-Amplitude Power System Point-on-Wave Measurements

The power grid is undergoing massive changes to ensure resiliency and reliability in a more decentralized world. Distributed energy resources are becoming a prominent source of generation, potentially leading to a lack of centralized generation sources. Due to these new behaviors and system topologies, it is important to install measurement devices that are 1) accurate and 2) self-aware of their measurement quality. In this paper, a residential-scale microgrid is used to generate voltage and current waveforms, captured by Verivolt and National Instruments measurement equipment. A least-squares approach is used to separate the “clean” signals from the noise. Finally, Gaussian mixture modeling is used to approximate noise distributions, and it is shown these higher-order distribution estimates are a better fit to voltage and current noise profiles than single-mode Gaussian estimates.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Process damping identification using Bayesian learning and time domain simulation

Process damping can provide improved machining productivity by increasing the stability limit at low spindle speeds. However, existing methods for identifying process damping models experimentally require specialized setups and/or multiple cutting tests. While the phenomenon is well known, the modeling challenges limit pre-process parameter selection that leverages the potential increases in material removal rates. This paper proposes a physics-informed Bayesian method that can identify the cutting force and process damping models from a limited set of test cuts without requiring direct measurements of cutting force or vibration. The method uses time domain simulation to incorporate process damping and provide a basis for test selection. Here, new strategies for efficient sampling and dimensionality reduction are applied to lower computation time and minimize the effect of model error. The proposed method is demonstrated and the identified cutting and damping force coefficients are compared to values obtained using machining tests and least-squares fitting.

42 ENGINEERING↗
DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗
DOE OSTI2023

Parameter Identification for Battery Abuse Reaction Kinetics Models Using DSC Analysis [SWR-23-87]

This code estimates the parameters as inputs for NREL’s abuse reaction kinetics model using Differential scanning calorimetry (DSC) experimental data. The parameters for calculating the rates of abuse reactions among battery cell components at elevated temperatures include frequency factor, activation energy, and reaction orders. The least-squared method is employed to fit the reaction model to DSC data. The code is implemented in MATLAB.

Yang, Chuanbo↗
DOE OSTI2024

XRF-XFS-XAS-Auto v1.0 - Beta release

This software allows to analyze XRF maps, XFS spectra and XAS spectra collected at the Advanced Light Source's Beamline 10.3.2. Features include: 1) XRF maps: - process XRF maps, all elemental maps are saved as bmp automatically and labeled with the incident energy used, the scale bar is also labeled and can be controlled. - XRF elemental correlation plots, save the correlation plots automatically - Extract single or multiple transects in XRF maps on one or several regions of interest, each transect profile is numbered and saved in a corresponding folder, along with the corresponding maps showing transect location. 2) XFS spectra - save in log10 scale the XFS spectra, either a single or multiple files all at once. The files are saved as .bmp. - XFS spectra are labeled according to tabulated fluorescence emission lines. 3) XAS spectra - allows to plot individual scalers in the raw data. - allows calibration of the spectra using an Io internal glitch present in all spectra and performing 1st derivative. - Least-square linear combination fitting of XANES or extended XANES spectra using a database of standards using 1, 2 or 3 components maximum. It also provides the 5 top combinations and provide the user for the possibility of saving the 2nd, 3rd, 4th and 5th best combinations in addition to the best one. The processed spectra (pre-edge background substracted, post-edge normalized), the fits and residuals are automatically saved. A table of the component, with fit% and SSN is provided and saved automatically as well.

Fakra, Sirine↗
DOE OSTI2026

Single-shot picosecond pump coherent Rayleigh scattering thermometry

A single-shot coherent Rayleigh scattering (CRS) technique capable of measurement times less than 10 ns is presented. Here, the use of a mode-locked picosecond pump laser yields repeatable electrostrictive forcing compared to previous CRS experiments using unseeded nanosecond pump pulses, which are beset by shot-to-shot variations. Quantitative measurements are achieved by dispersing the CRS signal onto an EMCCD sensor using a virtually imaged phased array and comparing the experimental spectra to an existing kinetic model with a least-squares fitting routine. Measurements are demonstrated at ambient and low-pressure (2 Torr), low-temperature (100 K) conditions where the CRS measurement is within the collisionless regime. Single-shot statistics indicated precision and accuracy within 4% at ambient conditions and within 8% at low density and temperature conditions. This single-shot CRS technique is a powerful diagnostic tool with potential for multi-parameter measurements in complex flow environments, including high-speed aerodynamic ground test facilities.

Senior, William Charles Bowman [Sandia National La↗
DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗
DOE OSTI2024

Development and Validation of Home Comfort System for Total Performance Deficiency/Fault Detection and Optimal Comfort Control

In this project, we developed and tested a learning-based home thermal model that facilitates the operation of a model predictive control (MPC)-based optimization agent and an automated fault detection and diagnosis (AFDD) agent. The home thermal model was constructed using a two-node resistor-capacitor model. Moreover, two accompanying parameter identification methods were introduced, least-squares and optimization. Based on the home thermal model, the MPC-based optimization agent was developed to optimize residential HVAC operation. Using two FDD methods, the AFDD agent was constructed to detect and diagnose two prevalent residential AC faults, airflow reduction and refrigerant undercharge. The home thermal model, along with the MPC-based optimization agent and AFDD agent, were tested at the Norman Test House, Miami Test House, Pacific Northwest National Laboratory (PNNL) Test House A, and PNNL Test House B. Finally, they were also field tested in nine demonstration homes with real occupants.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Neutron Positioning and Geometric Distortion Correction on the SNS SiPM Anger Camera

Neutron Anger cameras are scintillator-based thermal neutron detectors that utilize pixelated photosensors to read out visible light signals and position neutrons accurately They are versatile detectors that can cover large areas for diffraction instruments and offer high efficiency and sub-millimeter spatial resolution. Photomultiplier Tube (PMT) based cameras are installed on three instruments at Spallation Neutron Source (SNS). The next generation camera uses Silicon Photomultipliers (SiPMs) instead of PMTs, which allows for a more compact design and higher spatial resolution. In this report, the Gaussian least-squares position fitting method is described in detail, as well as the method used to correct for geometric distortions across the face of the camera. Results from neutron camera tests before and after the distortion correction are shown and the spatial resolution is quantified.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Estimation of Fission Product Transport Parameters for Cesium in the AGR-3/4 TRISO Fuel Experiment

A one-dimensional (1D) finite-element model of fission product transport in the AGR-3/4 experiment has been developed using the Multiphysics Object Oriented Simulation Environment (MOOSE) framework and implemented in the fuel performance code, BISON. The model resolves capsule-specific geometries, materials, and temperature histories and simulates radial migration of fission products from the fuel compact through the inner ring, outer ring, and into the sink ring. Model parameters governing diffusion and sorption were estimated for key fission products – cesium (Cs), and europium (Eu) – by simultaneously fitting modeled isotopic concentration profiles and total ring inventories to a post-irradiation experimental measurement. These data include gamma scanning, liquid scintillation for Sr-90, radial deconsolidation leach-burn-leach analysis, tomographic reconstructions, and destructive physical sampling. A mortar-based interfacial sorption framework was implemented to enforce physically consistent mass transfer and flux conservation across gas gaps. Two classes of parameter sets were derived: a least-squares best-fit, and a safety-oriented conservative-fit, what applies strong penalties for underprediction of sink inventories. Across all twelve capsules, the model successfully reproduces the dominant radial transport trends for Cs, Sr, with decreasing concentrations from the compact outward through successive rings. Cs behavior is captured most consistently, while strontium predictions reveal systematic trade-offs between compact accuracy and conservative sink-ring bounding. The results demonstrate that sink ring weighted calibration provides conservative, safety relevant bounds on low temperature fission product transport, but at the cost of underpredicting compact inventories for Sr isotopes. These discrepancies highlight the need for additional physics, including fast-slow diffusion model, incorporating trapping mechanism in the transport behavior. Overall, this work establishes a robust, capsule-specific modeling framework for AGR-3/4 fission product transport and provides a defensible basis for parameter selection in source-term and fuel performance analyses for high temperature gas-cooled reactors.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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↗