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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Baryon number violation: from nuclear matrix elements to BSM physics

Processes that violate baryon number, most notably proton decay and $n\bar{n}$ transitions, are promising probes of physics beyond the Standard Model (BSM) needed to understand the lack of antimatter in the Universe. To interpret current and forthcoming experimental limits, theory input from nuclear matrix elements to UV complete models enters. Thus, an interplay of experiment, effective field theory, lattice QCD, and BSM model building is required to develop strategies to accurately extract information from current and future data and maximize the impact and sensitivity of next-generation experiments. Here, we briefly summarize the main results and discussions from the workshop ‘INT-25-91W: Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics,’ held at the Institute for Nuclear Theory, University of Washington, Seattle, WA, 13–17 January 2025.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

IEEE 123-Bus System A Matrix

System component matrix for IEEE 123 bus distribution system for dynamic simulations.

Sahu, Vibhuti [Oak Ridge National Laboratory] (ORC↗
DOE OSTI2025

R-matrix School 2025: Introduction to R-matrix Theory

This technical memo serves as a lecture material for the R-matrix school 2025 and distributed among the participants. The manuscript discusses in details the introduction to the R-matrix theory including its algorithm to calculate reaction cross sections and derivation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Architecture-Aware Models of AI Engines for High-Performance Matrix Matrix Multiplication

The AI Engine (AIE) architecture, available in systems from mobile SoCs to server-class FPGAs, aims to efficiently execute AI/ML tasks through a two-dimensional array of compute tiles. Previous work on AIEs has explored different approaches to mapping computation across spatial arrays, but the compute kernel running on each tile has not been the focus. Additionally, the AIE-ML architecture introduces memory tiles and omits programmable logic, requiring new approaches to staging and moving data throughout the array. In this work we update analytical models developed for CPUs to produce the design of high performance kernels while introducing new model considerations such as memory structure, throughput, and latency as required by the AIE hardware. We evaluate our models by developing AIE-ML kernels for matrix multiplication in low-precision data types showing performance up to 95% of compute peak for the kernel when data resides in local memory and above 90% of compute peak when data resides in main memory.

Binder, Elliott D. [Carnegie Mellon University, Pi↗
DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

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

SAGA1 and MITH1 produce matrix-traversing membranes in the CO2-fixing pyrenoid

Abstract Approximately one-third of global CO 2 assimilation is performed by the pyrenoid, a liquid-like organelle found in most algae and some plants. Specialized pyrenoid-traversing membranes are hypothesized to drive CO 2 assimilation in the pyrenoid by delivering concentrated CO 2 , but how these membranes are made to traverse the pyrenoid matrix remains unknown. Here we show that proteins SAGA1 and MITH1 cause membranes to traverse the pyrenoid matrix in the model alga Chlamydomonas reinhardtii . Mutants deficient in SAGA1 or MITH1 lack matrix-traversing membranes and exhibit growth defects under CO 2 -limiting conditions. Expression of SAGA1 and MITH1 together in a heterologous system, the model plant Arabidopsis thaliana , produces matrix-traversing membranes. Both proteins localize to matrix-traversing membranes. SAGA1 binds to the major matrix component, Rubisco, and is necessary to initiate matrix-traversing membranes. MITH1 binds to SAGA1 and is necessary for extension of membranes through the matrix. Our data suggest that SAGA1 and MITH1 cause membranes to traverse the matrix by creating an adhesive interaction between the membrane and matrix. Our study identifies and characterizes key factors in the biogenesis of pyrenoid matrix-traversing membranes, demonstrates the importance of these membranes to pyrenoid function and marks a key milestone toward pyrenoid engineering into crops for improving yields.

Hennacy, Jessica H.↗
DOE OSTI2026

Quantum Time-Space Tradeoffs for Matrix Problems

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems—including matrix-vector product, matrix inversion, matrix multiplication and powering—existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms with at most a constant factor loss. For example, for almost all fixed matrices 𝐴, including the discrete Fourier transform matrix, we prove that quantum circuits with at most 𝑇 input queries and 𝑆 qubits of memory require 𝑇 = Ω⁢(𝑛 2 /𝑆) to compute matrix-vector product 𝐴⁢𝑥 for 𝑥 ∈{0,1 𝑛 . We similarly prove that matrix multiplication for 𝑛 ×𝑛 binary matrices requires 𝑇 = Ω⁢(𝑛 3 /$\sqrt{𝑆}$). Because many of our lower bounds are matched by deterministic algorithms with the same time and space complexity, our results show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity—the sum of the space per layer of a circuit. We also consider Boolean (i.e., AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for 𝑛 × 𝑛 Boolean matrix multiplication to 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/4 ) from 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/2 ). Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem that was the basis for prior work. To obtain our tight lower bounds for linear algebra problems, we require much stronger bounds than strong direct product theorems. We obtain these bounds by adding a new bucketing method to the quantum recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

lower bounds↗
DOE OSTI2025

Technical Considerations on MURR Control Blade Design Change and Testing using a New Metal Matrix Composite

The University of Missouri Research Reactor (MURR) is one of six research reactors, including a critical facility, that are pursuing conversion as part of a collaboration with the U.S. Department of Energy National Nuclear Security Administration Material Management and Minimization Office of Reactor Conversion and Uranium Supply, under the U.S. High Performance Research Reactors (USHPRR) conversion project. Five of the six USHPRR are planned to convert from highly enriched uranium (HEU) fuel using a low-enriched uranium (LEU) high assay monolithic alloy of uranium-10 wt% molybdenum (U-10Mo). As part of the conversion safety analysis, it is necessary to demonstrate the safety performance of the proposed core fueled with LEU as compared to the current HEU cores. The MURR reactor is planning to switch to a new control blade design that uses a metal matrix composite of boron carbide (B 4 C) and aluminum as the absorber in place of Boral®. Since MURR is expected to adopt the new metal matrix composite control blade design prior to conversion, the impact of the new blade design on the neutronics characteristics of the MURR cores for conversion are analyzed in this work through updates to incorporate the changes to the blade design in conversion models as they directly impact the LEU conversion safety analysis. The quantitative comparison shows that the neutronics and thermal hydraulic behavior of one metal matrix composite blade replacing a Boral blade is comparable for the two example MURR LEU and HEU cores states considered. Geometrical changes in the metal matrix composite blade design, combined with a 4% increase in areal boron density, showed local heating effects up to 20% higher than the Boral design. As expected, the metal matrix composite showed slightly lower heat depositions and absorber region temperatures for the LEU cases compared to HEU. Although this analysis was comparative for a single blade, maximum control blade temperatures for both Boral, metal matrix composite, and HEU/LEU remained below 100 °C, though additional analysis at a core level could differ. A qualitative irradiation behavior assessment concludes that the mechanisms that may drive swelling and blistering in the current Boral design are eased by the adoption of the metal matrix composite design. The work concludes that the two blade designs are essentially equivalent with regards to neutronics, thermal hydraulics, and expected material behavior under irradiation. However, due to the geometrical changes to the blades including redesigned and thinner cladding, new testing and increased surveillance for distortion and swelling are recommended to confirm the performance of the metal matrix composite control blade design. Where testing is completed prior to conversion, the only anticipated impacts on conversion to LEU U-10Mo fuel would be the need for models and safety analysis incorporating the metal matrix composite control blades.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Parametric matrix models

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate physical systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation.

Computational science↗
DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗
DOE OSTI2026

Powers of magnetic graph matrix: Fourier spectrum, walk compression, and applications

Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, nonequilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles—counts of graph walks indexed by the number of edge reversals. Crucially, we establish that walk profiles correspond to a Fourier transform of magnetic matrix powers. The connection allows exact reconstruction of walk profiles from magnetic matrix powers at multiple discrete potentials, and more importantly, an even smaller number of potentials often suffices for accurate approximate reconstruction in real networks. This shows the empirical compressibility of the information captured by the magnetic matrix. This fresh perspective suggests further applications; for example, we illustrate how powers of the magnetic matrix can identify frustrated directed cycles (e.g., feedforward loops) and can be effectively employed for link prediction by encoding local structural details in directed graphs.

complex networks↗
DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗
DOE OSTI2025

Matrix Diffusion Controls Mountain Hillslope Groundwater Ages and Inferred Storage Dynamics

Groundwater age distributions provide fundamental insights on coupled water and biogeochemical processes in mountain watersheds. Field-based studies have found mixtures of young and old-aged groundwater in mountain catchments underlain by bedrock; yet, the processes that dictate these groundwater age distributions are poorly understood. In this work, we use the coupled ParFlow-CLM integrated hydrologic and EcoSLIM particle tracking models to simulate groundwater age distributions on a lower montane hillslope in the East River Watershed, Colorado (USA). We develop a convolution-based approach to propagate fracture-matrix diffusion processes to the EcoSLIM advection-dominated age distributions. We compare observed 3 H and 4 He concentrations from two groundwater wells against model predictions that have varying advective transport times and matrix diffusion magnitudes. Based on a Monte Carlo analysis that considers uncertain matrix and fracture parameters, we find that matrix diffusion is needed to jointly predict 3 H and 4 He observations at both wells. The advection-dominated age distributions lack adequate mixing of young and old-aged water to capture the observed co-occurrence of 3 H and 4 He. The model scenario that best matches the 3 H, 4 He, and water level observations when considering both advective flowpath and matrix diffusion mixing processes has a dynamic bedrock groundwater reservoir that is susceptible to considerable storage losses during low-snow periods. This dynamic groundwater system amplifies the need to assimilate deeper bedrock groundwater into watershed hydro-biogeochemical predictions. This work further highlights the importance of considering matrix diffusion when interpreting environmental tracers in bedrock groundwater systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Polymer-fiber-reinforced polymers with enhanced interfacial bonding between polypropylene fiber and polyethylene matrix

Self-reinforced composites (SRCs) consist of reinforcing fibers and a base matrix made of the same thermoplastic polymer, offering lightweight, recyclability, and sustainability benefits. However, limited research exists on composites where the reinforcing thermoplastic polymer fibers differ from the base thermoplastic matrix. Here, this study focuses on investigating the mechanical behavior of such composites and exploring different surface modification methods to enhance the fiber/matrix interfacial bonding using polypropylene fibers and a polyethylene matrix as an example. It is shown that surface treatment with a commercial adhesion promoter containing n-butyl acetate significantly improves the interfacial shear strength between polypropylene fibers and the polyethylene matrix, increasing it by 145% compared to other methods investigated. Additionally, increasing the length of the embedded polymer fiber in the matrix leads to a notable increase in specific interfacial energy. Consequently, the thermoplastic polymer-fiber-reinforced polymers (PFRPs) using surface-treated woven polypropylene fabrics and a polyethylene matrix exhibit a 20% higher tensile strength and a 65% higher toughness compared to non-treated PFRPs. This study also shows that specific mechanical properties (normalized by the composite density) of the investigated woven PFRPs are similar to those of non-treated SRCs under uni-axial tension. Particularly, their ductility outperforms carbon-/glass-/aramid-fiber-reinforced polymers by at least 6 times at a same fiber volume fraction. The investigation of such composites and the exploration of surface modification methods present important progress in the field of thermoplastic PFRPs, which serve as a solution for addressing concerns related to recyclability and sustainability.

Fiber pull-out↗