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Results for “matrix completion”

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 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2023

Feeder Power Disaggregation: A Data-Efficient Matrix Completion Approach

This paper presents a data-driven algorithm for the feeder power disaggregation problem in distribution systems. Leveraging spatio-temporal power patterns in residential homes, residential power is discomposed into three components: sparse-switching loads, periodic loads, and photovoltaic (PV) generation, which are characterized through the design of two sparse matrices and a low-rank matrix. The matrix completion process is data-efficient because of the matrix sparsity and low rankness, along with the use of power system models. The proposed approach is tested using real-world residential data set on a 33-bus distribution system, demonstrating accurate power disaggregation with efficient matrix completion.

distribution system↗
NASA NTRS1993

Axisymmetric micromechanics of elastic-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modeled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying the Tsai-Hill yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying the Tresca yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: fiber yield, followed by matrix yielding; complete matrix yield, followed by fiber yielding; and partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.

Lee, Jong-Won↗
DOE OSTI2026

Correlated purification for restoring 𝑁-representability in quantum simulation

Experimentally measured reduced density matrices (RDMs) often violate constraints that ensure they represent N-electron states—known as N-representability conditions—because of statistical and hardware noise. In this work, we present a correlated purification framework based on semidefinite programming to restore the accuracy of a noisy, unphysical two-electron RDM (2-RDM). The method performs a bi-objective optimization that minimizes both the many-electron energy and the nuclear norm of the correction to the measured 2-RDM. The nuclear norm, often employed in matrix completion, promotes low-rank corrections, while the energy term acts as a regularization term that can improve the purity of the ground state. While the method is particularly effective for ground states, it can also be applied to excited and nonstationary states by decreasing the weight of the energy relative to the error norm. In an application to fermionic shadow tomography of large hydrogen chains, correlated purification yields substantial reductions in both energy and 2-RDM error, achieving chemical accuracy across dissociation curves. This framework provides a robust strategy for tomography in many-body quantum simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Transplatformer: translating toxicogenomic profiles between generations of platforms

Background Transcriptomic profiling technologies have advanced the analysis of biological and toxicological responses. However, substantial differences in probe design, dynamic range, gene coverage, and preprocessing pipelines across platforms introduce artifacts that limit cross-study integration and hinder the reuse of historical datasets. We aim to develop computational methods for accurate cross-platform translation to maximize the value of legacy resources. Results We present TransPlatformer a deep learning framework for translating gene expression profiles across heterogeneous toxicogenomics platforms. TransPlatformer employs a novel attention-based architecture to map high-dimensional fold-change vectors from legacy microarray technologies to current platforms. Models are trained and evaluated using DrugMatrix, spanning three technological generations. We investigate mixed-tissue, single-tissue, and cross-tissue training paradigms and benchmark performance against multilayer perceptron and matrix-completion baselines. In mixed-tissue training, TransPlatformer achieves a greater than 50% reduction in mean absolute error (0.043 vs. 0.09) and nearly doubles Pearson correlation ( ≈ 0.71 vs. 0.37) relative to baseline methods. Importantly, TransPlatformer preserves rare but biologically meaningful over- and under-expressed signals, with mean absolute error below 0.22. Single-tissue models yield further improvements for well-represented organs, such as a 10% reduction in liver mean absolute error, while underscoring the need for data augmentation strategies in low-sample tissues.ra Conclusions TransPlatformer provides an effective and scalable computational solution for cross-platform transcriptomic translation. By enabling biologically faithful harmonization of gene expression data, the proposed approach facilitates the reuse of legacy toxicogenomics datasets, enhances downstream biomarker discovery, and supports more reproducible predictive modeling in toxicology.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1976

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Putney, B. H.↗
NASA NTRS1977

Data collecting activities of the 'Outlook for Space' Panel

The paper describes the work of the 'Outlook for Space' Panel, a NASA-wide study group concerned with the role space flight might play in American society during the years approaching 2000. The study considers the progression of projects from 'could do' (for which capability exists), to 'should do' (because of social benefits), to 'will do' (unknown at this time). Opinions as to objectives were solicited from NASA personnel, advisory committees, industrial organizations, and academic theoreticians. Poll data was examined. A large-scale survey of the attitudes of young people toward the future and space was also undertaken, and a complete matrix is presented of themes (such as production and management of food and forestry resources) and theme subcategory specific activities (for example, global crop production), versus the students' perceived areas of national interest or benefit (e.g., expansion of human knowledge).

Stroud, W. G.↗
NASA NTRS1984

Helicopter model rotor-blade vortex interaction impulsive noise: Scalability and parametric variations

Acoustic data taken in the anechoic Deutsch-Niederlaendischer Windkanal (DNW) have documented the blade vortex interaction (BVI) impulsive noise radiated from a 1/7-scale model main rotor of the AH-1 series helicopter. Averaged model scale data were compared with averaged full scale, inflight acoustic data under similar nondimensional test conditions. At low advance ratios (mu = 0.164 to 0.194), the data scale remarkable well in level and waveform shape, and also duplicate the directivity pattern of BVI impulsive noise. At moderate advance ratios (mu = 0.224 to 0.270), the scaling deteriorates, suggesting that the model scale rotor is not adequately simulating the full scale BVI noise; presently, no proved explanation of this discrepancy exists. Carefully performed parametric variations over a complete matrix of testing conditions have shown that all of the four governing nondimensional parameters - tip Mach number at hover, advance ratio, local inflow ratio, and thrust coefficient - are highly sensitive to BVI noise radiation.

Splettstoesser, W. R.↗
NASA NTRS1985

Helicopter model rotor-blade vortex interaction impulsive noise - Scalability and parametric variations

Acoustic data taken in the anechoic Deutsch-Niederlaendischer Windkanal (DNW) have documented the blade vortex interaction (BVI) impulsive noise radiated from a 1/7-scale model main rotor of the AH-1 series helicopter. Averaged model scale data were compared with averaged full scale, inflight acoustic data under similar nondimensional test conditions. At low advance ratios (mu = 0.164 to 0.194), the data scale remarkable well in level and waveform shape, and also duplicate the directivity pattern of BVI impulsive noise. At moderate advance ratios (mu = 0.224 to 0.270), the scalig deteriorates, suggesting that the model scale rotor is not adequately simulating the full scale BVI noise; presently, no proved explanation of this discrepancy exists. Carefully performed parametric variations over a complete matrix of testing conditions have shown that all of the four governing nondimensional parameters - tip Mach number at hover, advance ratio, local inflow ratio, and thrust coefficient - are highly sensitive to BVI noise radiation.

Boxwell, D. A.↗
NASA NTRS1985

Universal Keplerian state transition matrix

A completely general method for computing the Keplerian state transition matrix in terms of Goodyear's universal variables is presented. This includes a new scheme for solving Kepler's problem which is a necessary first step to computing the transition matrix. The Kepler problem is solved in terms of a new independent variable requiring the evaluation of only one transcendental function. Furthermore, this transcendental function may be conveniently evaluated by means of a Gaussian continued fraction.

Shepperd, S. W.↗
NASA NTRS2011

Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix

In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.

Llama, Eduardo Garcia↗
NASA NTRS1993

Ceramic matrix composites properties/microstresses with complete and partial interphase bond

A multilevel substructuring technique which includes a unique fiber substructuring concept is used for the analysis of continuous fiber reinforced ceramic matrix composites. This technique has four levels of substructuring--from laminate to ply, to supply, and then to fiber. A stand-alone computer code CEMCAN (Ceramic Matrix Composites Analyzer), incorporating this technique and specifically for the simulation of ceramic matrix composites behavior, is currently under development at NASA Lewis Research Center in Cleveland, Ohio. The thermal and mechanical properties, along with the microstresses, for a SiC/RBSN (silicon carbide fiber and reaction bonded silicon nitride matrix) composite at different fiber volume ratios and varying degrees of interfacial bond around the fiber circumference are computed. Values predicted by CEMCAN computer code are shown to bound the experimentally measured values. Results also show that transverse tensile strength test can be a sensitive test method to assess interfacial conditions.

Mital, Subodh K.↗
DOE OSTI2024

Mild chemical recycling of carbon fiber-reinforced epoxy composites in aqueous buffers and development of hydrothermally recyclable vitrimer composites from recyclates

Carbon fiber-reinforced polymer (CFRP) composites have gained widespread adoption across diverse industries. However, their inherent stability, stemming from the crosslinked structure of the matrix resin, poses a significant challenge in managing the growing volume of CFRP waste. Consequently, there is a pressing need for an eco-friendly upcycling method that effectively recovers and reuses both the valuable carbon fibers and the polymer matrix from CFRP waste. This study presents a novel approach for upcycling CFRP waste under environmentally friendly conditions. Firstly, CFRP waste with an amine-cured epoxy matrix was completely decomposed in aqueous buffer solutions under mild conditions (≤ 220 °C, pH = 4.8). Further, decomposed matrix polymer (DMP) was employed to transform conventional epoxy resins into recyclable vitrimers. Lastly, new composites that can be hydrothermally recycled were fabricated using both DMP and recovered carbon fibers. As a result, this work proposes a novel strategy for achieving a circular economy within the CFRP industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Practical preventive reliability using matrix forms

This paper describes a practical new tool to improve the reliability of equipment. It uses a matrix form to help monitor anticipated component faults precisely. The tool provides the practical measures necessary to generate matrix tables that accurately display all causes of failure and all planned programmatic analyses, tests, processes, and inspections. When completed, the matrix tables give users in-depth visibility of the degree of protection against component failure that is provided by the program's preventive measure plans. The matrix form is an excellent technique for tracking, and thereby influencing, the reliability of nonelectronic spacecraft subsystems or components. No electronic applications have been tried, but the procedure can be useful in the electronics field, e.g., in integrated circuit production planning, and perhaps in process control, inspection or test lines for other electronic components. The drawing of forms, and the recording/manipulation of the data can be computerized.

Johnson, S. A.↗
NASA NTRS1981

A pad perturbation method for the dynamic coefficients of tilting-pad journal bearings

A pad assembly method for analyzing tilting-pad bearings is presented. The method results in the complete coefficient matrix for a tilting-pad bearing; the matrix is independent of the pad inertia, the pitch frequency and the number of degrees of freedom of the pad. A pad assembly method is used because it allows the collection of more bearing data with less computer time than a brute force iterative procedure. The results given show the complete dynamical matrices for a five-pad tilting-pad bearing both including and ignoring the damping effects of the unloaded (top) pads. For a symmetrical tilting-pad bearing the reduced cross-coupling coefficients are zero when the moment of inertia of the pad is ignored.

Allaire, P. E.↗