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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Efficient CP Rounding Using Alternating Least Squares with QR Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is widely used for analyzing multidimensional data, and the alternating least squares (CP-ALS) algorithm is a common method for its computation. CP rounding is the problem of computing a lower-rank CP decomposition of an input already in a higher-rank CP format. While the normal equations (NE) approach in CP-ALS is efficient for the CP rounding problem and frequently used, it becomes unstable in the presence of ill-conditioned subproblems. This paper presents a new QR-based CP-ALS method for CP rounding that preserves both numerical stability and computational efficiency. Here, our experiments show that the proposed method offers significant speedup over a previous QR-based approach and the Tensor Toolbox's NE-based implementation, particularly for higher-order tensors. Furthermore, our approach demonstrates a marked reduction in error for ill-conditioned problems, with error reductions several orders of magnitude smaller compared to the NE-based method, while achieving faster convergence and more accurate solutions. By using a more numerically stable approach, we can solve more problems in reduced working precision, which enables further reduction in time to solution.

CANDECOMP/PARAFAC↗
DOE OSTI2023

CP decomposition for tensors via alternating least squares with QR decomposition

The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low-rank structure in multidimensional data. Computing a CP decomposition via an alternating least squares (ALS) method reduces the problem to several linear least squares problems. The standard way to solve these linear least squares subproblems is to use the normal equations, which inherit special tensor structure that can be exploited for computational efficiency. However, the normal equations are sensitive to numerical ill-conditioning, which can compromise the results of the decomposition. In this paper, we develop versions of the CP-ALS algorithm using the QR decomposition and the singular value decomposition, which are more numerically stable than the normal equations, to solve the linear least squares problems. Our algorithms utilize the tensor structure of the CP-ALS subproblems efficiently, have the same complexity as the standard CP-ALS algorithm when the input is dense and the rank is small, and are shown via examples to produce more stable results when ill-conditioning is present. Our MATLAB implementation achieves the same running time as the standard algorithm for small ranks, and we show that the new methods can obtain lower approximation error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Use of Fisher's Ratio assisted multivariate curve resolution- alternating least squares for discovery-based analysis using ultrahigh pressure liquid chromatography-high resolution mass spectrometry

Non-targeted analysis of complex chemical mixtures can be difficult considering the convoluted nature of the matrix and the potential unknown chemical differences between samples or classes of samples. Ultrahigh pressure liquid chromatography coupled to quadrupole time-of-flight mass spectrometry (UHPLC-QTOF) is an ideal technique to probe chemical differences for a wide variety of samples. While UHPLC-QTOF can discover minute chemical differences down to low part per billion (ppb) concentrations with a high degree of confidence, the application of high-resolution mass spectrometry can yield massive amounts of information (∼ 10 gb per sample) that cannot be analyzed manually. Therefore, the application of chemometric techniques is mandatory for the interrogation of complex samples. Fisher's ratio (FR) assisted multivariate curve resolution-alternating least squares (MCR-ALS) was used to the discover and identify the chemical differences between two classes of materials: 1) a pond water matrix and 2) the matrix spiked with a pharmaceutical standard mix containing 17 compounds. Thirteen of the seventeen spiked compounds were discovered using FR analysis, and then five were successfully deconvoluted using MCR-ALS wherein the number of curves chosen were automatically determined using singular value decomposition (SVD). In conclusion, the use of an automated FR assisted MCR-ALS will aid in discovering trace levels of chemical components without the need for the researcher to provide potentially biased input which will aid in non-targeted workflow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The controlling role of atmosphere in dawsonite versus gibbsite precipitation from tetrahedral aluminate species

In highly alkaline solution, aluminum speciates as the tetrahedrally coordinated aluminate monomer, Al(OH)4- and/or dimer Al2O(OH)62-, yet precipitates as octahedrally coordinated gibbsite (Al(OH)3). This tetrahedral to octahedral transformation governs Al precipitation, which is crucial to worldwide Al production, and to the processing of caustic high-level radioactive wastes. Despite its significance, the transformation pathway remains unknown. Here we explore the roles of atmospheric water and carbon dioxide in mediating the transformation of the tetrahedrally coordinated potassium aluminate dimer salt (K2Al2O(OH)6) to gibbsite versus potassium dawsonite (KAl(CO3)(OH)2). A combination of in-situ attenuated total reflection infrared spectroscopy, ex-situ micro X-ray diffraction, and multivariate curve resolution-alternating least squares chemometrics analysis reveals that humidity plays a key role in the transformation by limiting the amount of alkalinity neutralization by dissolved CO2. Lower humidity favors higher alkalinity and incorporation of carbonate species in the final Al product to form KAl(CO3)(OH)2. Higher humidity enables more acid generation that destabilizes dawsonite and favors gibbsite as the solubility limiting phase. Because the transformation was restricted to occur in thin water films, the results suggest that transition from tetra- to octahedrally coordinated Al does not have to occur in bulk solution, as has often been hypothesized, but may instead appear on the source mineral surface.

Dembowski, Mateusz↗
DOE OSTI2020

The Fe 4+ / 3+ Redox Mechanism in NaFeO 2 : A Simultaneous Operando Nuclear Resonance and X-ray Scattering Study

Simultaneous operando Nuclear Forward Scattering and transmission X-ray diffraction and 57 Fe Mössbauer spectroscopy measurements were carried out in order to investigate the electrochemical mechanism of NaFeO 2 vs. Na metal using a specifically designed in situ cell. The obtained data were analysed using an alternative and innovative data analysis approach based on chemometric tools such as Principal Component Analysis (PCA) and Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS). This approach, which allows the unbiased extraction of all possible information from the operando data, enabled the stepwise reconstruction of the independent “real” components permitting the description of the desodiation mechanism of NaFeO 2 . This wealth of information allows a clear description of the electrochemical reaction at the redox-active iron centres, and thus an improved comprehension of the cycling mechanisms of this material vs. sodium.

25 ENERGY STORAGE↗
DOE OSTI2023

New methods for trace analysis of gamma-irradiated pentaerythritol tetranitrate

High explosives (HEs) are used in a diverse range of applications in which they could be exposed to various radiation levels that may cause potential chemical changes. This study further evaluated pentaerythritol tetranitrate (PETN) that was previously aged with a low-level 2 kGy dose of gamma irradiation in order to understand chemical changes caused by irradiation. Both unirradiated PETN and gamma-irradiated PETN were analyzed using ultra high-pressure liquid chromatography coupled to quadrupole time of flight mass spectrometry (UHPLC-QTOF). The resulting data were processed in a non-targeted manner using Fisher's ratio analysis and multivariate curve resolution-alternating least squares (MCR-ALS) to aid in discovery and identification of the chemical changes brought about by irradiation without a priori knowledge. The application of using UHPLC-QTOF in combination with chemometric techniques for the analysis of irradiated samples has not previously been performed. Here, in this work, we show how to use this method to provide chemical information that would otherwise not be discernible, such as the discovery of degradation of the various homologues of PETN. Major differences identified with radiolytic aging of the PETN sample included decomposition products that resulted from the degradation of the trigger linkage – the O–NO 2 bonds – resulting in the formation of alcohol and aldehyde groups. Similar degradation was also observed in the PETN homologues as well as interconversion from one homologue to another.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Temporal Ni K-Edge X-ray Absorption Spectroscopy Study Reveals the Kinetics of the Ni Redox Behavior of the Iron-Nickel Oxide Bimetallic OER Catalyst

Operando X-ray absorption spectroscopy (XAS) can be utilized to probe the phase and structural changes of FeNiOx and similar transition metal oxide electrocatalysts during electrocatalytic reactions. However, capturing the temporal changes occurring in the operando chemistry of electrocatalysts has been little studied. Here, in this work, we successfully capture the time-resolved changes at the Ni K-edge for both the X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) regions of an aqueous phase synthesized FeNiO x bimetallic nanoparticle electrocatalyst. During a stepped voltage experiment, the temporal change in the Ni K-edge was observed as the applied voltage was stepped from 0.7 to 0.8 V versus the silver/silver chloride reference electrode, and the change observed is associated with the Ni redox transition from the 2+ to 3+/4+ oxidation state. Individual XAS spectra were obtained in 90 s, and a total of 9 scans post voltage step showed a unique transition from a hydroxide to an oxyhydroxide phase. The shift in absorption edge energy position and the changes in spectral shape for individual scans explain the typically observed broadening of the Ni K-edge XANES spectrum during time-averaged operando XAS, and a kinetic analysis revealed a first-order observed rate constant, |k obs |, of 0.00426 s –1 and a half-life (t 1/2 ) of 163 s. Multivariate curve resolution-alternating least squares analysis followed by linear combination fitting analysis for time-averaged versus time-resolved Ni K-edge changes upon voltage step show distinct differences in estimated contributions from Ni 2+ oxide/hydroxide phases. Detailed EXAFS modeling shows the phase transition from hydroxide to oxyhydroxide on top of the unchanged metallic core.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Quantifying the Impact of Metal Population Distribution in MFI-Supported Mo Catalysts for Methane Dehydroaromatization

Precise evaluation of intrinsic kinetic behavior in Mo/MFI catalysts for methane dehydroaromatization (MDA) is confounded by variations in Mo dispersion and speciation, which are influenced by metal loading and zeolite acidity. This work advances the utility of H 2 -temperature programmed reduction (H 2 -TPR) for characterizing Mo/MFI catalysts by enabling quantitative comparison of MoO x populations distinguished by reduction behavior and linked to initial catalytic performance. A comprehensive H 2 reduction pathway is established through systematic H 2 - TPR studies varying catalyst composition (1–10 wt % Mo, Si/Al = 15, 40, ∞), supplemented by UV-Raman spectroscopy, X-ray powder diffraction, N 2 physisorption, NH 3 -TPD, and advanced spectroscopic analysis (in situ XAS with principal component analysis/multivariate curve resolution—alternating least squares). Two low-temperature H 2 -TPR regions capture distinct Mo populations undergoing initial Mo(VI)→Mo(IV) reduction: a lower-temperature population (Mo-RI) associated primarily with highly dispersed, anchored MoO x species expected to predominantly reside within MFI channels, and a higher-temperature population (Mo-RII) corresponding to a broader set of MoO x species that becomes increasingly bulk-like/extrazeolitic at higher Mo loading. Quantification of these populations provides practical, kinetically relevant descriptors for comparing initial MDA rates across catalysts with varying Mo loading, Si/Al ratio, and MoO x heterogeneity. Application of lower-temperature Mo-RI estimates to kinetic measurements reveals a minimum threshold of ∼0.12 × 10 –3 mol Mo-RI/g cat , above which initial forward benzene rates normalized to this population converge despite differences in metal loading and zeolite Brønsted acidity. This threshold coincides with a transition toward a common C 2 -mediated benzene-forming regime, as indicated by approach-to-equilibrium analysis of methane-to-ethane, ethane-to-ethylene, and ethylene-to-benzene reaction steps. Above this threshold, normalized initial benzene rates are nearly invariant with increasing Mo-RII/Mo-RI population ratio, indicating that excess Mo-RII populations, including bulk-like/extrazeolitic MoO x domains present at higher loading, do not measurably suppress benzene formation associated with anchored and mostly channel-confined Mo population under the initial-rate conditions examined.

Mo/MFI↗
DOE OSTI2020

Operando structural and chemical evolutions of TiS 2 in Na-ion batteries

Titanium disulfide (TiS 2 ) with high electric conductivity, fast rate capability, and good cycling performance is a promising candidate for electrode material in sodium (Na)-ion batteries. Despite the well-studied electrochemical behaviors of TiS 2 in Li-ion batteries, the detailed reaction mechanism of TiS 2 in Na-ion batteries is not yet fully understood due to a more complex multi-phase conversion process. In this work, reactions of TiS 2 in Na-ion batteries are investigated via a multi-modal synchrotron approach: operando X-ray Absorption Spectroscopy (XAS) – including X-ray Absorption Near-Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) – and ex situ X-ray Powder Diffraction (XPD), coupled with computational modeling. Operando XANES spectra indicate that the redox reactions occur in both Ti and S during the electrochemically driven phase transformation. Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis of XAS suggests that different numbers of components are involved in the lithiation and sodiation of TiS 2 , with the sodiation including at least one intermediate phase in addition to the starting material and the final sodiation product. Ex situ XPD and Rietveld refinement further determined and quantified the unknown phases, showing that three phases, TiS 2 , Na 0.55 TiS 2 , and NaTiS 2 , participate in the sodiation of TiS 2 . Operando EXAFS results show the changes in the Ti–Ti coordination number and interatomic distance. This explains the coulombic efficiency decay due to the incomplete recovery of the coordination number of Ti after cycling. Overall, this work reveals the reaction mechanism occurring in Na–TiS 2 batteries with a greater quantitative understanding of the structural evolution. By combining the multi-modal synchrotron approach and computational work, this study provides a framework for studying a broader range of electrochemically driven phase-transformation systems towards advanced energy storage and conversion applications.

25 ENERGY STORAGE↗
DOE OSTI2024

BioXTAS RAW 2 : new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI ; updated automated Guinier fitting and D max finding algorithms; automated series ( e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares ( REGALS ); creation of electron-density reconstructions using electron density via solution scattering ( DENSS ); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantifying neptunium oxidation states in nitric acid through spectroelectrochemistry and chemometrics

Controlled-potential in situ thin-layer spectropotentiometry was leveraged to generate visible/near-infrared (VIS/NIR) absorption spectral data sets for the development of chemometric models to quantify Np(III/IV/V/VI) oxidation states in HNO 3 . This technology would be valuable in laboratory studies and when monitoring process solutions to guide feed adjustments for radiochemical separations—the performance of which depends on oxidation state. This approach successfully isolated and stabilized Np species in pure (~99%) oxidation states without compromising solution optical properties. Multivariate curve resolution–alternating least squares models were evaluated to resolve spectral and component concentrations from a scan that sequentially produced Np(VI), Np(V), Np(IV), and Np(III) spectra with mixtures of two valences at a time. Although it provided a useful approximation, the method was not able to quantitively resolve each component likely because of rotational ambiguity. Additionally, partial least squares regression models were built from artificial and electrochemically generated VIS/NIR spectral training sets to study the effect of interionic interactions on spectral characteristics. Models built with true Bi-chemical mixtures of coexisting Np oxidation states and spectra generated from additive combinations of pure end points had similar prediction performance. This methodology can be used to directly quantify Np concentration and the ratio of Np oxidation states and other actinides in remote settings such as hot cells.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Distributed-Memory Parallel JointNMF

Joint Nonnegative Matrix Factorization (JointNMF) is a hybrid method for mining information from datasets that contain both feature and connection information. We propose distributed-memory parallelizations of three algorithms for solving the JointNMF problem based on Alternating Nonnegative Least Squares, Projected Gradient Descent, and Projected Gauss-Newton. We extend well-known communication-avoiding algorithms using a single processor grid case to our coupled case on two processor grids. We demonstrate the scalability of the algorithms on up to 960 cores (40 nodes) with 60% parallel efficiency. The more sophisticated Alternating Nonnegative Least Squares (ANLS) and Gauss-Newton variants outperform the first-order gradient descent method in reducing the objective on large-scale problems. We perform a topic modelling task on a large corpus of academic papers that consists of over 37 million paper abstracts and nearly a billion citation relationships, demonstrating the utility and scalability of the methods.

Eswar, Srinivas↗
NASA NTRS1997

Low Speed, 2-D Rotor/Stator Active Noise Control at the Source Demonstration

Wake/blade-row interaction noise produced by the Annular Cascade Facility at Purdue University has been modeled using the LINFLO analysis. Actuator displacements needed for complete cancellation of the propagating acoustic response modes have been determined, along with the associated actuator power requirements. As an alternative, weighted least squares minimization of the total far-field sound power using individual actuators has also been examined. Attempts were made to translate the two-dimensional aerodynamic results into three-dimensional actuator requirements. The results lie near the limit of present actuator technology. In order to investigate the concept of noise control at the source for active rotor/stator noise control at the source, various techniques for embedding miniature actuators into vanes were examined. Numerous miniature speaker arrangements were tested and analyzed to determine their suitability as actuators for a demonstration test in the Annular Cascade Facility at Purdue. The best candidates demonstrated marginal performance. An alternative concept to using vane mounted speakers as control actuators was developed and tested. The concept uses compression drivers which are mounted externally to the stator vanes. Each compression driver is connected via a tube to an air cavity in the stator vane, from which the driver signal radiates into the working section of the experimental rig. The actual locations and dimensions of the actuators were used as input parameters for a LINFLO computational analysis of the actuator displacements required for complete cancellation of tones in the Purdue experimental rig. The actuators were designed and an arrangement determined which is compatible with the Purdue experimental rig and instrumentation. Experimental tests indicate that the actuators are capable of producing equivalent displacements greater than the requirements predicted by the LINFLO analysis. The acoustic output of the actuators was also found to be unaffected by the presence of air flow representative of the Purdue experimental rig. A test of the active noise control at the source concept for rotor/stator active noise control was demonstrated. This 2-D test demonstrated conclusively the simultaneous reduction of two acoustic modes. Reductions of over 10 dB were obtained over a wide operating range.

Simonich, John C.↗