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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2026

Is the Matrix Completion of Reduced Density Matrices Unique?

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce the computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina’s theorem (Rosina, M. Queen’s Papers on Pure and Applied Mathematics , 1968, No. 11, 369), we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum–stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi–Hubbard model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The DYRKP1 kinase regulates cell wall degradation in Chlamydomonas by inducing matrix metalloproteinase expression

Abstract The cell wall of plants and algae is an important cell structure that protects cells from changes in the external physical and chemical environment. This extracellular matrix, composed of polysaccharides and glycoproteins, must be constantly remodeled throughout the life cycle. However, compared to matrix polysaccharides, little is known about the mechanisms regulating the formation and degradation of matrix glycoproteins. We report here that a plant kinase belonging to the dual-specificity tyrosine phosphorylation-regulated kinase (DYRKP1) family present in all eukaryotes regulates cell wall degradation after mitosis of Chlamydomonas reinhardtii by inducing the expression of matrix metalloproteinases. Without DYRKP1, daughter cells cannot disassemble parental cell walls and remain trapped inside for more than 10 days. On the other hand, the dual-specificity tyrosine phosphorylation-regulated kinase complementation lines show normal degradation of the parental cell wall. Transcriptomic and proteomic analyses indicate a marked downregulation of MMP gene expression and accumulation, respectively, in the dyrkp1 mutants. The mutants deficient in matrix metalloproteinases retain palmelloid structures for a longer time than the background strain, like dyrkp1 mutants. Our findings show that dual-specificity tyrosine phosphorylation-regulated kinase, by ensuring timely MMP expression, enables the successful execution of the cell cycle. Altogether, this study provides insight into the life cycle regulation in plants and algae.

Kim, Minjae (ORCID:0000000223561295)↗
DOE OSTI2025

Microstructure and bonding between calcium aluminate cement‐containing gahnite–alumina matrix and refractory aggregates

Calcium aluminate cement enhances the thermomechanical properties of refractory castables through the formation of acicular calcium hexaluminate (CaO·6Al 2 O 3 ), Ca 2 Mg 2 Al 28 O 46 (CAM-I), and CaMg 2 Al 16 O 27 (CAM-II) phases in MgO- or MgAl 2 O 4 -containing castables. The compatibility of CA 6 with gahnite (ZnAl 2 O 4 ), and acicular Ca 2 Zn 2 Al 28 O 46 (CAZ-I) and CaZn 2 Al 16 O 27 (CAZ-II) phases formation have been previously reported. Here, in this work, the interaction between a CAC binder containing ZnAl 2 O 4 -Al 2 O 3 matrix with commonly used refractory aggregates such as tabular alumina (TA), alumina-rich (AR90, AR78) and stoichiometric (SM72) MgAl 2 O 4 spinels, and fused and dead-burned magnesia (FM, DBM, respectively) were investigated at 1650°C for 5 h. Microstructural analysis, using digital microscopy, scanning electron microscopy, and energy dispersive spectroscopy, revealed the formation of acicular CaZn 0.18 Al 11.82 O 18.91 , CAZ-I and CAZ-II grains, and strong interfacial bonding between the matrix and TA and spinel aggregates. FM and DBM were found to debond from the matrix. Thick interface layers were observed between the matrix and all the aggregates but TA. Null hypothesis significance testing (NHST) shows that the difference in the number of acicular grains between the interface zone and the bulk matrix (Z) is statistically significant for AR90/Z, SM72/Z, FM/Z, and DBM/Z interfaces, but not significant for TA/Z and AR78/Z. The role of the aggregates’ chemistry on the interfacial bonding and microstructure evolution is discussed.

Ramteke, Rajat Durgesh [Univ. of Alabama, Birmingh↗
DOE OSTI2026

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗
DOE OSTI2025

Modular-Invariant Random Matrix Theory and AdS 3 Wormholes

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL⁡(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

conformal field theory↗
DOE OSTI2025

Lanczos algorithm for lattice QCD matrix elements

Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Infinite matrix product states for (1 + 1)-dimensional gauge theories

We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD 2 .

confinement↗
DOE OSTI2025

Multi-material ALE remap with interface sharpening using high-order matrix-free finite element methods

The arbitrary Lagrangian-Eulerian (ALE) technique involves remapping field quantities from a Lagrangian mesh to an optimized mesh in a conservative, accurate and bounds-preserving manner. For methods based on arbitrary order finite elements, as described in a reference, material volume fractions are advected in pseudo-time using flux-corrected transport (FCT) without any form of interface reconstruction. In practice, this can lead to excessive propagation of small volume fractions throughout the domain. In addition, this method requires assembly of a global advection matrix to compute the bounds-preserving low-order FCT solution. In this work, we introduce a new approach for ALE remap using a high-order matrix-free technique which incorporates a flux modification to sharpen material interfaces in a conservative manner. Our approach begins with computing a bounds-preserving low-order solution to the ALE remap equations at the element level. We then compute a sharp interface solution (not guaranteed to be bounds-preserving) which comes from solving an augmented version of the ALE remap equations with a conservative flux modification which acts to sharpen material volume fractions based on their gradients and transport directions. Using the sharp interface solution, we make global corrections to the bounds-preserving solution while maintaining preservation of bounds. By blending with the sharpened solution at the global level we are able to globally conserve mass without hindering the remap pseudo-time step. This new interface-aware ALE remap method is based entirely on partial assembly techniques where globally assembled matrix operators are no longer needed, resulting in a globally matrix-free FCT method for multi-material, multi-field ALE remap with high performance on GPU architectures. We present results of our new remap method on 1D, 2D and 3D benchmarks and describe the algorithmic tailoring for GPU architectures that was developed.

Vargas, Arturo [Lawrence Livermore National Labora↗
DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Bayesian event categorization matrix approach for explosion monitoring

Current efforts to correctly categorize natural events from suspected explosion sources with data that is collected by ground- or space-based sensors presents historical challenges that remain unaddressed by the Event Categorization Matrix (ECM) model. Smaller historical events (lower yield explosions) may have data available from fewer measurement techniques than are available today, and therefore, a historical event record can lack a complete set of discriminants. The covariance structures can also differ between such observations of event (source-type) categories. Both obstacles are problematic for the classic ECM model. Our work addresses this gap and presents a Bayesian update to the previous ECM model, termed the Bayesian Event Categorization Matrix model, which can be trained on partial observations and does not rely on a pooled covariance structure. We further augment the ECM model with Bayesian Decision Theory so that false negative or false positive rates of an event categorization can be reduced in an intuitive manner. To demonstrate improved categorization rates for the Bayesian Event Categorization Matrix model, we compare an array of Bayesian and classic models with multiple performance metrics using Monte Carlo experiments. We use both synthetic and real data. Our Bayesian models show consistent gains in overall accuracy and lower false negative rates relative to the classic ECM model. Here, we propose future avenues to improve Bayesian Event Categorization Matrix models’ decision making and predictive capability.

58 GEOSCIENCES↗
DOE OSTI2025

RE-INTEGRATE EMT Simulation Software: Graph Convolutional Network for Sparse Matrix Pattern Detection

The increasing complexity of power networks, driven by proliferation of inverters, presents analytical challenges that simplified models often fail to capture, necessitating Electromagnetic Transient (EMT) simulations. EMT models are represented as discretized differential-algebraic equations (DAEs), forming a linear system Ax = b that is computationally intensive to solve. Due to inherent sparsity of adjacency matrix A, distinct patterns emerge that, when accurately identified, enable efficient solver selection to minimize computation time. However, identifying ideal pattern is complicated by numerous reordering algorithms and limited structural insights. To address this, we introduce a Graph Convolutional Network (GCN) model for classifying sparse matrix patterns common in power system analysis. The model, achieving 96% test accuracy, is validated using PV plant models of 125 MW capacities connected to New England 39-bus transmission system (TS), and further scaled to a 4,992-bus network with 384 PV plants, yielding 191, 616 × 191, 616 sized A matrix. For all cases, the GCN model accurately identifies the matrix’s intrinsic sparse pattern, demonstrating its potential to enhance solver performance in EMT analysis.

Hossain, Md Rifat [Florida International Universit↗
DOE OSTI2024

FTTN: Feature-Targeted Testing for Numerical Properties of NVIDIA & AMD Matrix Accelerators

FTTN is a test suite to evaluate the numerical behaviors of matrix accelerators of GPUs (NVIDIA Tensor Cores and AMD Matrix Cores) in a quick and simple setting. Matrix accelerators are heavily used in today's computationally intense applications to speed up matrix multiplications. This test suite provides a comprehensive study on the numerical behaviors of these accelerators, including support for subnormals, rounding modes, extra precision bits and FMA features. Is there

Laguna Peralta, Ignacio↗
DOE OSTI2026

Testing of High S Matrix Glasses to Expand DFHLW Glass Compositional Ranges (Rev.1)

Gaps in glass composition-property data for direct-feed high-level waste (DFHLW) have recently been identified. One such gap is the region of high sulfur solubility since previous, pretreated, high-level wastes contained very little sulfur. Filling this data gap will significantly broaden the range of process flowsheet options including minimal washing and will allow for optimized waste loading in DFHLW glasses. This report summarizes the data collected during the characterization of the DFHLW High S Glass Matrix (HS24). A glass matrix of 50 glass compositions was developed to evenly cover the DFHLW composition region for high sulfur glass. Matrix glasses were designed to expand the composition region outside the current component concentration and property limits so as to reduce uncertainties at the limits. The 50 matrix glasses were fabricated and tested for properties important to the success of DFHLW vitrification including: compositions, canister centerline cooling (CCC) crystallinity and isothermal crystallinity, density, viscosity, electrical conductivity (EC), product consistency test (PCT) response, toxicity, and sulfate solubility. Melter materials corrosion testing is reported elsewhere. These glasses were intentionally designed to have high SO 3 solubilities (0.7 to 2.2 SO 3 wt%) in compositional regions that had not been previously explored. Forty-eight glasses showed the measured SO 3 content retained >80% of the target SO 3 and the densities of all the glasses ranged from 2.49 g·cm -3 to 2.74 g·cm -3 . While the model predicted nepheline formation in 5 glasses, one of the tested 50 CCC glasses formed nepheline, and 35 glasses formed Cr-containing phases such as spinels and eskolaite. Only five glasses were amorphous after CCC treatment where 44 glasses with detectable crystals contained =10 wt% crystals and only one glass had > 10 wt% crystals. None of the glasses exceeded the allowable T 2% for spinel crystal formation at 950 ºC (i.e., no glasses had >2 wt% spinel at 950 ºC) during isothermal crystal fraction tests where 10 glasses showed no crystalline phases at or below 950 ºC. All the glasses (except one which failed being slightly lower than the target) satisfied the SO 3 constraint while 98 glasses did not meet the viscosity constraints and 4 failed the EC constraints. Six quenched (Q) and six CCC glasses failed the Defense Waste Processing Facility (DWPF) Environmental Assessment (EA) glass PCT threshold and 3 Q and 4 CCC failed the PCT design constraint. One glass exceeded the WTP delisting limits for Cr via EPA Method 1311 (i.e., Toxicity Characteristic Leaching Procedure, TCLP). It should be emphasized that some of these glasses were specifically designed to approach or even exceed certain property constraints, as filling data gaps in these regions will provide the greatest benefit for future model development by improving accuracy and reducing uncertainties. These insights will ultimately support the development of more robust glass formulation strategies, enabling higher waste loading, reducing operational risks, and expanding the processing envelope.

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

Scaling up the transcorrelated density matrix renormalization group

Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their application to larger systems has been hampered by the computational cost. We develop improved techniques for the transcorrelated density-matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrate large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. Our developments stem from three technical inventions: (i) constructing matrix product operators (MPOs) of transcorrelated Hamiltonians with low bond dimension and high sparsity, (ii) exploiting the entanglement structure of the ground states to increase the accuracy of the MPS representation, and (iii) optimizing the nonlinear parameter of the Gutzwiller correlator to mitigate the nonvariational nature of the transcorrelated method. Here, we examine systems of size up to 12×12 lattice sites, four times larger than previous transcorrelated DMRG studies, and demonstrate that transcorrelated DMRG yields significant improvements over standard nontranscorrelated DMRG for equivalent computational effort. Transcorrelated DMRG reduces the error of the ground-state energy by 2.4×–14×, with the smallest improvement seen for a small system at half filling and the largest improvement in a dilute closed-shell system.

Density matrix renormalization group↗
DOE OSTI2025

Spatially Resolved Raman Spectroscopy of Thin Carbon Interphase in SiC Ceramic Matrix Composites

A dedicated analysis method is presented to extract the Raman spectrum of an interphase layer thinner than the laser spot size. We focused on spatial correlations between the contrast of optical micrographs and Raman hyperspectral data to predict the constituents of the mixed spectra measured near the interphase. By employing a mapping step size of 0.1 μm, the Raman spectrum of approximately 0.3-μm-thick carbon interphase in a SiC fiber-reinforced SiC matrix composite was extracted from data acquired with a theoretical spot size of about 0.7 μm. Notably, conventional chemometrics procedures were unable to isolate the interphase signal, instead producing a spectrum representing a mixture of interphase and matrix. This study used another composite with approximately 0.9-μm-thick interphase to validate the analysis method, enabling direct measurement of the interphase spectrum. The proposed Raman analysis method has advantages in specimen volume and turnaround time compared to traditional characterization methods, such as transmission electron microscopy. In conclusion, this study also evaluates the applicability of the analysis method to different composite materials and identifies key requirements of the measurements, including the ratio of interphase thickness to spot size and the homogeneity of the surrounding matrix.

ceramic matrix composite↗
DOE OSTI2026

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

Extended Supersymmetry↗