Search NASA⌕ Search

SEARCH · Search NASA

Results for “TENSOR ANALYSIS”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

GFCCLib: Scalable and efficient coupled-cluster Green's function library for accurately tackling many-body electronic structure problems

Coupled-cluster Green’s function (GFCC) calculation has drawn much attention in the recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. However, GFCC calculations on scientific computing clusters usually suffer from expensive higher di- mensional tensor contractions in the complex space, expensive inter-process communi- cation, and severe load imbalance, which limits it’s routine use for tackling electronic structure problems. Here we present a numerical library prototype that is specifically designed for large-scale GFCC calculations. The design of the library is focused on a systematically optimal computing strategy to improve its scalability and efficiency. The performance of the library is demonstrated by the relevant profiling analysis of running GFCC calculations on remote giant computing clusters. The capability of the library is highlighted by computing a wide near valence band of a fullerene C60 molecule for the first time at the GFCCSD level that shows excellent agreement with the experimental spectrum.

Peng, Bo↗
NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗
NASA NTRSDate not supplied

A Machine Learning Model for Solar Sail Shape Reconstruction Using Flight Data

Solar sail deformation leads to disturbance torques from solar radiation pressure, driving performance requirements for momentum management systems. For the Solar Cruiser technology demonstrator mission, we have developed a model leveraging neural network-based machine learning to derive sail shape characteristics. The model uses torque and attitude telemetry simulated from a reduced-order tensor model of the deformed sail mesh over a characterization sequence. The machine learning model predicts sail boom deflection with comparable accuracy to that of an onboard context camera. This model can discover sail shape with no additional mass or data downlink requirements, allowing for validation of sail force modeling assumptions using in flight data. The results from the project hold promise for the further implementation of machine learning techniques in solar sail telemetry analysis and control.

solar sail↗
NASA NTRSDate not supplied

A Machine Learning Model for Solar Sail Shape Reconstruction Using Flight Data

Solar sail deformation leads to disturbance torques from solar radiation pressure, driving performance requirements for momentum management systems. For the Solar Cruiser technology demonstrator mission, we have developed a model leveraging neural network-based machine learning to derive sail shape characteristics. The model uses torque and attitude telemetry simulated from a reduced-order tensor model of the deformed sail mesh over a characterization sequence. The machine learning model predicts sail boom deflection with comparable accuracy to that of an onboard context camera. This model can discover sail shape with no additional mass or data downlink requirements, allowing for validation of sail force modeling assumptions using in flight data. The results from the project hold promise for the further implementation of machine learning techniques in solar sail telemetry analysis and control.

solar sail↗
DOE OSTI2020

Research Introduction [Slides]

In the topic of Reverse Time Imaging, we proposed a new IC to reduce computation cost but reserve image resolution for distributed sensor networks. For Induced Seismicity in Oklahoma, we analyzed fault stress state analysis at state scale, and we applied machine learning techniques to polarity picking and seismicity rate forecasting. The results provide better understanding of fault properties, stress field, and the relationships among fault, stress state, injections, and potential seismic hazards. Lastly, for Microseismic Monitoring, we detected and located 770 low-frequency events (5-50 Hz): (1) Shallow events are highly clustered, consistent with the pathway from injection well 13-10A to monitoring well; moment tensor inversion shows dominant tensile cracking; (2) Deep events are scattered and show migration pattern to the basement; moment tensors show that most events are shear cracks.

58 GEOSCIENCES↗
DOE OSTI2022

Hidden conformal symmetries from Killing towers with an application to large-D/CFT

We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. We build the SL(2, R) generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. Our construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: we use the Killing tower to build a novel tensor equation connecting the SL(2,R) Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions we recover previously known results that were obtained using the ``near-region'' limit and the monodromy method. We then perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. We also extend this analysis to the large-dimensional Schwarzschild black hole as a step towards buliding a Large-D/CFT correspondence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Optimizing Distributed Training on Frontier for Large Language Models

Large language models (LLMs) have demonstrated remarkable success as foundational models, benefiting various downstream applications through fine-tuning. Loss scaling studies have demonstrated the superior performance of larger LLMs compared to their smaller counterparts. Nevertheless, training LLMs with billions of parameters poses significant challenges and requires considerable computational resources. For example, training a one trillion parameter GPT-style model on 20 trillion tokens requires a staggering 120 million exaflops. This research explores efficient distributed training strategies to extract this computation from Frontier, the world's first exascale supercomputer. We enable and investigate various model and data parallel training techniques, such as tensor parallelism, pipeline parallelism, and sharded data parallelism, to facilitate training a trillion-parameter model on Frontier. We empirically assess these techniques and their associated parameters to determine their impact on memory footprint, communication latency, and GPU's computational efficiency. We analyze the complex interplay among these techniques and find a strategy to combine them to achieve high throughput through hyperparameter tuning. We have identified efficient strategies for training large LLMs of varying sizes through empirical analysis and hyperparameter tuning. For 22 Billion, 175 Billion, and 1 Trillion parameters, we achieved GPU throughputs of 38.38%, 36.14%, and 31.96%, respectively. For the training of the 175 Billion parameter model and the 1 Trillion parameter model, we achieved 100% weak scaling efficiency on 1024 and 3072 Mi250X GPUs, respectively. We also achieved strong scaling efficiencies of 89% and 87% for these two models. We trained these models only tens of iterations instead of training till completion.

Yin, Junqi↗
DOE OSTI2025

Magnetic pair distribution function and half polarized neutron powder diffraction at the HB-2A powder diffractometer

Local magnetic order and anisotropy are often central for understanding fundamental behavior and emergent functional properties in quantum materials and beyond. Advances in neutron powder diffraction experiments and analysis tools now allow for quantitative determination. Here, we demonstrate this here with complementary total neutron scattering and polarized neutron measurements on the HB-2A neutron powder diffractometer at the High Flux Isotope Reactor (HFIR). In recent years, magnetic pair distribution function (mPDF) analysis has emerged as a powerful technique for probing local magnetic spin ordering of magnetic materials. This method can be broadly applied to any magnetic material but is particularly effective for studying systems with short-range magnetic order, such as materials with reduced dimensionality, geometrically frustrated magnets, thermoelectrics, multiferroics, and correlated paramagnets. Magnetic anisotropy often underpins the short-range order adopted. Half-polarized neutron powder diffraction (pNPD) can be used to determine the local susceptibility tensor on the magnetic sites to quantify the magnetic anisotropy. Combining the techniques of mPDF and pNPD can therefore provide valuable insights into local magnetic behavior. A series of measurements optimized for these techniques are presented as exemplar cases focused on frustrated materials where short-range order dominates, these include measurements to ultra-low temperature (<100 mK) not typically accessible for such experiments.

Half polarized neutron scattering↗
DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Multi-Scale Analysis of Effective Mechanical Properties of 3D Woven Composite Materials

This work aims to compute and analyze the mechanical properties of 3D woven composite materials that share the same yarn structure but differ in their matrix porosity and fiber volume fraction. Assuming linear elastic behavior, the software PuMA, developed at NASA, was used to characterize the different composites from their constituents' data averaging their elastic properties in three main directions to obtain their effective orthotropic mechanical properties. This was performed in three steps: firstly, the different phases (yarns/matrix) were analyzed as anisotropic materials separately at the micro-scale; then, the results from these analyses were homogenized and used to obtain the anisotropic elasticity tensor at the meso-scale for the different woven materials; and finally, assuming orthotropic mechanical behavior for the unit cell the mechanical properties were obtained at the macro-scale. The 3D woven composite materials selected for this study are made of phenolic resin with porosity values between 0 and 0.6, and resin infiltrated carbon fiber with volume fractions between 0.5 and 0.9 for the yarns. Results from PuMA were validated with external FEA simulations for the non-porous 3D woven material with a fiber volume fraction of 0.9 in the yarns. Results will be included in the final paper after completing the study detailed in Section II.

Sergio Fraile Izquierdo↗
DOE OSTI2021

COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior

This paper presents a deep learning framework for epidemiology system identification from noisy and sparse observations with quantified uncertainty. The proposed approach employs an ensemble of deep neural networks to infer the time-dependent reproduction number of an infectious disease by formulating a tensor-based multi-step loss function that allows us to efficiently calibrate the model on multiple observed trajectories. The method is applied to a mobility and social behavior-based SEIR model of COVID-19 spread. The model is trained on Google and Unacast mobility data spanning a period of 66 days, and is able to yield accurate future forecasts of COVID-19 spread in 203 US counties within a time-window of 15 days. Interestingly, a sensitivity analysis that assesses the importance of different mobility and social behavior parameters reveals that attendance of close places, including workplaces, residential, and retail and recreational locations, has the largest impact on the effective reproduction number. Furthermore, the model enables us to rapidly probe and quantify the effects of government interventions, such as lock-down and re-opening strategies. Taken together, the proposed framework provides a robust workflow for data-driven epidemiology model discovery under uncertainty and produces probabilistic forecasts for the evolution of a pandemic that can judiciously provide information for policy and decision making. All codes and data accompanying this manuscript are available at https://github.com/PredictiveIntelligenceLab/DeepCOVID19.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2004

Estimation of Dynamical Parameters in Atmospheric Data Sets

In this study a new technique is used to derive dynamical parameters out of atmospheric data sets. This technique, called the structure tensor technique, can be used to estimate dynamical parameters such as motion, source strengths, diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. The fundamental algorithm will be extended to the analysis of multi- channel (e.g. multi trace gas) image sequences and to provide solutions to the extended aperture problem. In this study sensitivity studies have been performed to determine the usability of this technique for data sets with different resolution in time and space and different dimensions.

Wenig, Mark O.↗
DOE OSTI2021

Propagation Pattern for Moment Representation of the Lattice Boltzmann Method

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

42 ENGINEERING↗
NASA NTRS1993

The radiated noise from isotropic turbulence revisited

The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order Tij retarded-time covariance is evaluated from the square of similar second order covariance, which is assumed known. In this derivation, no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions.

Lilley, Geoffrey M.↗
DOE OSTI2021

Performance of the rigorous renormalization group for first-order phase transitions and topological phases

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in one-dimensional systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau [Nat. Phys. 11, 566 (2015)1745-247310.1038/nphys3345]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first-order phase transitions and in symmetry-protected topological phases. Our study is motivated by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first-order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near-)degenerate manifolds. Furthermore, the rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines well-ordered, accurate energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The well-tempered cosmological constant: the Horndeski variations

Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest— not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Octet and decuplet baryon σ terms and mass decompositions

We present a comprehensive analysis of the SU(3) octet and decuplet baryon masses and σ terms using high-precision lattice QCD data and chiral SU(3) effective theory with finite range regularization. The effects of various systematic uncertainties, including from the scale setting of the lattice data and the regularization prescriptions, are quantified. We find the pion-nucleon and strange nucleon σ terms to be σ πN = 44(3)(3) MeV and σ Ns = 50(6)(1) MeV, respectively. Furthermore, the results provide constraints on the energy-momentum tensor mass decompositions of the SU(3) octet and decuplet baryons, where we find that the trace anomaly and quark-gluon energies decrease for strange baryons due to their larger strange σ terms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1979

Nonlinear temperature dependent failure analysis of finite width composite laminates

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

Nagarkar, A. P.↗