Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix multiplication”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Evaluation of fluxon synapse device based on superconducting loops for energy efficient neuromorphic computing

With Moore’s law nearing its end due to the physical scaling limitations of CMOS technology, alternative computing approaches have gained considerable attention as ways to improve computing performance. Here, we evaluate performance prospects of a new approach based on disordered superconducting loops with Josephson-junctions for energy efficient neuromorphic computing. Synaptic weights can be stored as internal trapped fluxon states of three superconducting loops connected with multiple Josephson-junctions (JJ) and modulated by input signals applied in the form of discrete fluxons (quantized flux) in a controlled manner. The stable trapped fluxon state directs the incoming flux through different pathways with the flow statistics representing different synaptic weights. We explore implementation of matrix–vector-multiplication (MVM) operations using arrays of these fluxon synapse devices. We investigate the energy efficiency of online-learning of MNIST dataset. Our results suggest that the fluxon synapse array can provide ~100× reduction in energy consumption compared to other state-of-the-art synaptic devices. This work presents a proof-of-concept that will pave the way for development of high-speed and highly energy efficient neuromorphic computing systems based on superconducting materials.

42 ENGINEERING↗

Performance Analysis and Optimal Node-aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. Furthermore, this is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

97 MATHEMATICS AND COMPUTING↗

Structural and Dynamical Roles of Bound Polymer Chains in Rubber Reinforcement

The addition of nanofillers to rubber matrices is a powerful route to improve the mechanical properties. Here, we focus on a molecular understanding of basic mechanisms that are important for the reinforcement in rubbers. The key role in this process is ascribed to bound rubber (BR) that engages with the matrix as well as with adjacent nanofillers. To date, this understanding has been impeded by the lack of experimental tools to directly probe the BR chains buried in a polymer matrix composed of the same polymer. To tackle this challenge, we combine neutron scattering/spectroscopy techniques with isotope-labeling and molecular dynamics simulations. The system is a simplified carbon-black-filled polybutadiene. The combined experimental and computational results provide new insights into the local structural and dynamical heterogeneities of BR chains and their interactions with the matrix polymer, highlighting (i) the structural partition of the bound chains into three components (i.e., trains, loops, and tails) and their fractions; (ii) their dynamical hierarchies, i.e., the trains that remain immobile on the filler surface, the loops that are fairly large and hence allow the interdigitation of matrix chains, and the tails with their unique characteristics to reach far out into the matrix and entangle with matrix chains. These multiple roles of the constituent components of the BR chains promote the formation of a well-developed adhesive polymer–filler interface, enhancing the elastic property of a filled rubber. Finally, the comprehensive understanding derived and validated by the model rubber will be translatable to many other polymer nanocomposites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution up to fifth order ⟨𝑥 4 ⟩ and for the skewness range [−0.33, 0] using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing 𝑎 = 0.04 fm and valence pion mass 300 MeV, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV 2 . We employ ratio-scheme renormalization and next-to-leading logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

Moments of parton distribution functions of any order from lattice QCD

We describe a procedure to determine moments of parton distribution functions of any order in lattice quantum chromodynamics (QCD). The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with the physical matrix elements can be obtained using continuum symmetries and the irreducible representations of Euclidean 4-dimensional rotations. We calculate the matching coefficients at one-loop in perturbation theory for moments of any order in the flavor nonsinglet case. We also give specific examples of operators that could be used in lattice QCD computations. It turns out that it is possible to choose operators with identical Lorentz indices and still have a multiplicative matching. One can thus use twist-2 operators exclusively with temporal indices, thus substantially improving the signal-to-noise ratio in the computation of the hadronic matrix elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Glauber-theory analysis of nuclear reactions on a 12 C target with variational Monte Carlo wave functions

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using ‘approximate’ Glauber theory whose validity is hard to evaluate. Here, we perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+¹²C, ⁴,⁶He+¹²C, and ¹²C+¹²C collisions. We use the variational Monte Carlo wave functions for ⁴,⁶He and ¹²C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber’s phase-shift function.

Horiuchi, W. [Osaka Metropolitan University (Japan↗

Properties and microstructure evolution of silicon nitride and zirconium nitride following Ni ion irradiation

We report that silicon nitride and zirconium nitride have been proposed as potential materials for multiple nuclear applications (inert matrix fuels, accident tolerant fuels, space nuclear power, fusion reactor design), yet knowledge on their behavior under irradiation remains limited. Ion irradiations were performed using 15 MeV Ni 5+ ions on Si 3 N 4 and ZrN samples, with midrange doses (around 3 µm) from 1 to 50 dpa and temperatures from 300 to 700°C. Volumetric lattice swelling was determined by grazing incidence X-ray diffraction, defect production and evolution were tracked using Transmission Electron Microscopy, and nanoindentation was performed to quantify the ceramics’ mechanical properties evolution. The results from these irradiation studies on nitride ceramics help fill the current gap present in the literature. Behavior consistent with past work on irradiated Si 3 N 4 was observed with respect to mechanical properties and defect formation up to 15 dpa and 500°C. Failure of the grain boundary sintering aid in Si 3 N 4 was observed above these conditions. Different behavior was observed in both nitrides at 50 dpa and 700°C, where lattice swelling increased past potential saturation values. Unreported cavity formation was witnessed in both materials under all irradiation conditions, with stable number density and slight size increase above 15 dpa. The mechanism for the cavity formation remains to be determined.

36 MATERIALS SCIENCE↗

Benefits of using multiple Raman laser wavelengths for characterizing defects in a UO 2 matrix

Abstract Raman spectroscopy is one of the most useful techniques for studying the structure of UO 2 and changes due to specific defects caused by doping, changes in stoichiometry, irradiation, or heating under oxidizing conditions. In this paper, we illustrate several aspects of the application of Raman techniques to the study of UO 2 , including the use of wavelength‐dependent excitation (455, 532, and 785 nm) to assess the effects of doping (Nd, Th, and Zr), ion irradiation, and in situ heating and oxidation (UO 2 to U 3 O 8 ). Additionally, we show examples of how correlative microscopy is possible using electron backscatter diffraction combined with Raman maps of specific vibration bands or of laser‐induced luminescence generated by rare‐earth dopants in the matrix. For each of these applications, we suggest optimal excitation wavelengths that vary depending on the desired data. Blue (455 nm) excitation tends to promote oxidation even at low powers, but because Raman spectra change little with doping, irradiation‐induced changes are easier to observe. Green (532 nm) excitation is optimal for observing electron–phonon resonance effects in UO 2 and offers a good compromise for high‐temperature oxidation experiments, delivering high‐quality spectra for both UO 2 and U 3 O 8 . Infrared (785 nm) excitation is best for observing “defect” bands associated with doping in UO 2 , as changes with irradiation are small. Raman spectroscopy is particularly suited for studying the stability of UO 2 towards oxidation in the presence of dopants simulating fission products, where electron–phonon resonant effects, dopant ion luminescence, and mapping can be used together to investigate structural rearrangement as a function of temperature. These techniques can offer insight into microstructural changes in UO 2 fuels at higher burnups envisioned in future reactors.

42 ENGINEERING↗

Generalized Mercier stability criterion for stellarators

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

Physics↗

Propulsion Electrification Architecture Selection Process and Cost of Carbon Abatement Analysis for Heavy-Duty Off-Road Material Handler

The heavy-duty off-road industry continues to expand efforts to reduce fuel consumption and CO 2 e (carbon dioxide equivalent) emissions. Many manufacturers are pursuing electrification to decrease fuel consumption and emissions. Future policies will likely require electrification for CO2e savings, as seen in light-duty on-road vehicles. Electrified architectures vary widely in the heavy-duty off-road space, with parallel hybrids in some applications and series hybrids in others. The diverse applications for different types of equipment mean different electrified configurations are required. Companies must also determine the value in pursuing electrified architectures; this work analyzes a range of electrified architectures, from micro hybrids to parallel hybrids to series hybrids to a BEV, looking at the total cost, total CO 2 e, and cost per CO 2 e (cost of carbon abatement, or cost of carbon reduction) using data for the year 2021. This study is focused on a heavy-duty off-road material handler, the Pettibone Cary-Lift 204i. This machine’s specialty application, including events like unloading large oil pipes from a railcar, requires a unique electrified architecture that suits its specific needs. However, the results from this study may be extrapolated to similar machinery to inform fuel savings options across the heavy-duty off-road industry. In this study, a unique electrified architecture is determined for the Cary-Lift. This architecture is informed by multiple rounds of a Pugh matrix decision analysis to select a shortened list of desirable electrified architectures. The shortened list is modeled and simulated to determine CO 2 e, cost, and cost per CO 2 e. A final architecture is determined as a plug-in series hybrid that reduces fuel consumption by 65%, targeting the large fuel and CO 2 e savings that are likely to be required for the future of the heavy-duty off-road industry.

33 ADVANCED PROPULSION SYSTEMS↗

Source identification by non-negative matrix factorization combined with semi-supervised clustering

Machine-learning methods and apparatus are provided to solve blind source separation problems with an unknown number of sources and having a signal propagation model with features such as wave-like propagation, medium-dependent velocity, attenuation, diffusion, and/or advection, between sources and sensors. In exemplary embodiments, multiple trials of non-negative matrix factorization are performed for a fixed number of sources, with selection criteria applied to determine successful trials. A semi-supervised clustering procedure is applied to trial results, and the clustering results are evaluated for robustness using measures for reconstruction quality and cluster separation. The number of sources is determined by comparing these measures for different trial numbers of sources. Source locations and parameters of the signal propagation model can also be determined. Disclosed methods are applicable to a wide range of spatial problems including chemical dispersal, pressure transients, and electromagnetic signals, and also to non-spatial problems such as cancer mutation.

Alexandrov, Boian S.↗

An Adaptive Multiparameter Penalty Selection Method for Multiconstraint and Multiblock ADMM

This work presents a new method for online selection of multiple penalty parameters for the alternating direction method of multipliers (ADMM) algorithm applied to optimization problems with multiple constraints or functions with block matrix components. ADMM is widely used for solving constrained optimization problems in a variety of fields, including signal and image processing. Implementations of ADMM often utilize a single hyperparameter, referred to as the penalty parameter, which needs to be tuned to control the rate of convergence. However, in problems with multiple constraints, ADMM may demonstrate slow convergence regardless of penalty parameter selection due to scale differences between constraints. Accounting for scale differences between constraints to improve convergence in these cases requires introducing a penalty parameter for each constraint. The proposed method is able to adaptively account for differences in scale between constraints, providing robustness with respect to problem transformations and initial selection of penalty parameters. It is also simple to understand and implement. Our numerical experiments demonstrate that the proposed method performs favorably compared to a variety of existing penalty parameter selection methods.

97 MATHEMATICS AND COMPUTING↗

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Interface instabilities in hafnium hydride entrained iron metal matrix composites

The chemical interactions in Fe–HfH 2 metal matrix composites (MMCs) are studied across multiple length scales to elucidate the decomposition of the parent phases and corresponding reaction zone physics during direct current sintering. Fe–HfH 2 composites were synthesized with increasing as-mixed hydride contents of Fe–25% HfH 2 , Fe–40% HfH 2 , Fe–55% HfH 2 , and Fe–70% HfH 2 (all in vol. %) to demonstrate the ability to achieve sintered MMCs with target hydride contents. Samples were probed across multiple length scales through a multi-modal workflow employing x-ray diffraction, scanning electron microscopy and segmentation analysis, and synchrotron techniques including hard x-ray fluorescence mapping and nanoprobe x-ray absorption near-edge structure measurements. Under the selected sintering temperature and pressure conditions, hydrogen evolution is seen to evolve through parallel paths: thermal decomposition from during the transformation of HfH 2 to HfH x<2 and through subsequent reaction with the Fe matrix leading to intermetallic phase formation. Specifically, HfFe and HfFe 2 intermetallic formation accelerates the release of hydrogen with a subsequent HfO 2 phase forming at grain boundaries. For this MMC, the consumption or loss of hydrogen can be considerable in compacts with initial hydride loading of 25%–40% HfH 2 approaching 83% hydrogen loss for the lower volume fraction composites. Increasing the volume fraction of HfH 2 to 70% enhanced the retained hydrogen content to 53% and attributed to the reduced interfacial area intrinsic to the increased HfH 2 loading in this MMC.

36 MATERIALS SCIENCE↗