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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Moment Tensor Inversion Toolkit

The MTINV toolkit (2002-present) is a collection of computer codes and applications written to invert for the moment tensor of a seismic source given the three components of ground motion recorded at regional seismic stations (e.g., Ichinose et al., 2003). The computer codes and workflow are organized to generate moment tensor solutions for a range of source depths and origin times because of the trade-off between these two quantities. The metric used is the variance reduction and variance reduction modulated by the percent double-couple to determine the best-fit moment-tensor solution. We can solve for a deviatoric moment tensor with a constraint added for no isotropic component although this constraint can be lifted for estimating the full moment tensor like mining collapses or explosion sources.

Ichinose, GeneA↗
DOE OSTI2018

Benchmarking treewidth as a practical component of tensor network simulations

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast tensor disentangling algorithm

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.

Slagle, Kevin↗
DOE OSTI2017

Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Effects of Stochastic Velocity Variations on Estimating Time Dependent Seismic Moment Tensors: Applications to the Blue Mountain Well Perforation Data

Resolving the time dependent terms in the seismic moment tensor provides important information that can be used to interpret the source process of an explosion, including the separation of isotropic explosion terms from shear forces and potentially isolated force couples. In this report, we detail our method of inverting three component seismic data for the seismic moment tensor. We review possible seismic source models from the simplest isotropic explosion type source to those incorporating the six independent moment tensor terms. The inversion we describe is formulated in the frequency domain, and results in estimates of time dependent moment tensor components. The inversion relies on an accurate estimate of the Green's functions of the Earth. However, given the complexity of the Earth, we explore the effects of inaccuracies in the presumed Earth model used to estimate the Green's functions needed for the inversion. Specifically, we explore the effects of stochastic variations in the Earth models on the inversion results. These tests are synthetic throughout, and show that adding stochastic density/velocity heterogeneity in the presumed Earth model results in reduced amplitude seismic moment tensor estimates, as well as degrading the data misfit. We suggest two mitigation strategies. First, produce a suite of Green's functions using different realizations of the stochastic field within the Earth Model. Secondly, perform the in- version in the power spectral domain, eliminating all phase information. Finally, we analyze actual seismic data collected in winter 2017/2018. The seismic data was collected at in active geothermal well site outside of Winnimucca, NV, and was produced during well stimulation operations. In general, the inversion results were poor, with a high degree of data misfit. We hypothesize that the poor results are a function of a poorly constrained Earth model as well as noisy, high-frequency data being used in the inversion.

58 GEOSCIENCES↗
DOE OSTI2023

Bayesian inference for the seismic moment tensor using regional waveforms and a data-derived distribution of velocity models

The largest source of uncertainty in any source inversion is the velocity model used to construct the transfer function employed in the forward model that relates observed ground motion to the seismic moment tensor. However, standard inverse procedures often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. We attempt to incorporate this uncertainty into an estimation of the seismic moment tensor using a distribution of velocity models calculated in a prior effort based on different and complementary data sets. The posterior distribution of velocity models is then used to construct Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional waveform data. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and can be interpreted in terms of most-probable source-type.

58 GEOSCIENCES↗
DOE OSTI2024

Journey to Time-Variable Moment Tensors through Inversion of Acoustic and Seismoacoustic Data

We explore the capability of acoustic and seismoacoustic datasets to directly resolve a complex, time-variable source consisting of a buried mechanism, represented as a moment tensor, and a spall mechanism, represented as a vertical force at the surface. Traditionally, each component of a resolved moment tensor assumes one underlying source time function, which likely fails to capture the full evolution of a dynamic source, such as an explosion followed by slip on near-source joints or development of spallation. Specifically, we expand previous work to resolve a time-variable moment tensor using single-modality and joint-modality inversion frameworks through analysis of infrasound and seismoacoustic data recorded as part of the Source Physics Experiment Phase II: Dry Alluvium Geology (DAG). We investigate the impact of including signals from seismic-to-air coupling that are local to each infrasound sensor in comparison to mainly atmosphere-propagating acoustic signals, which occur from coupling of the wavefield from the subsurface to the atmosphere directly above the source. Additionally, we assess the ability of our inversion algorithm to fit observed infrasound data using a variety of time-variable source mechanisms. First, we consider the buried moment tensor source alone, which assumes that the determined Green’s functions incorporate effects from spallation or that the impact from spallation is minimal. Second, we examine the estimated buried moment tensor and vertical surface spallation as terms that must both be resolved in the inversion. Third, we assess the ability for an estimated vertical surface spallation source to fit the acoustic data on its own. Finally, we compare results from the joint inversion of both seismic geophone and infrasound acoustic data for the buried-only source compared to buried and spallation sources. Our results are a preliminary investigation into the applications of the inversion technique to recorded datasets and show the technique has limited capabilities using acoustic data alone. Instead, this method shows promise for seismic and seismoacoustic datasets to resolve the time-variable mechanisms of a buried source.

47 OTHER INSTRUMENTATION↗
NASA NTRS1985

Nonlinear optimal control with tensors - Some computational issues

Some computational issues associated with the calcualtion of optimal feedback controls for nonlinear systems in a tensor setting are described. The specific issues addressed pertain to the combinatorial nature of the loading of the elements into tensors used to represent the system, cost, and feedback, and the subsequent calculations involving these elements. Particular attention is given to: the symmetric tensor algebra which is a natural setting for representing polynomials; the conversions between symmetric and nonsymmetric tensors; the general nature of the calculations required; and the solution equation for nonlinear optimal feedback control. It is concluded that nonlinear tensor feedback can improve performance both in terms of system responses and in terms of system stability region.

Osullivan, J. A.↗
NASA NTRS1992

The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization

Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.

Reifler, Frank↗
NASA NTRS1993

Tensoral: A system for post-processing turbulence simulation data

Many computer simulations in engineering and science -- and especially in computational fluid dynamics (CFD) -- produce huge quantities of numerical data. These data are often so large as to make even relatively simple post-processing of this data unwieldy. The data, once computed and quality-assured, is most likely analyzed by only a few people. As a result, much useful numerical data is under-utilized. Since future state-of-the-art simulations will produce even larger datasets, will use more complex flow geometries, and will be performed on more complex supercomputers, data management issues will become increasingly cumbersome. My goal is to provide software which will automate the present and future task of managing and post-processing large turbulence datasets. My research has focused on the development of these software tools -- specifically, through the development of a very high-level language called 'Tensoral'. The ultimate goal of Tensoral is to convert high-level mathematical expressions (tensor algebra, calculus, and statistics) into efficient low-level programs which numerically calculate these expressions given simulation datasets. This approach to the database and post-processing problem has several advantages. Using Tensoral the numerical and data management details of a simulation are shielded from the concerns of the end user. This shielding is carried out without sacrificing post-processor efficiency and robustness. Another advantage of Tensoral is that its very high-level nature lends itself to portability across a wide variety of computing (and supercomputing) platforms. This is especially important considering the rapidity of changes in supercomputing hardware.

Dresselhaus, Eliot↗
NASA NTRS1993

Visualizing second order tensor fields with hyperstreamlines

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

Delmarcelle, Thierry↗
DOE OSTI2026

QuadSync: Quadrifocal tensor synchronization via Tucker decomposition

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Miao, Daniel [University of Minnesota]↗
DOE OSTI2017

HPC formulations of optimization algorithms for tensor completion

Tensor completion is a powerful tool used to estimate or recover missing values in multi-way data. It has seen great success in domains such as product recommendation and healthcare. Tensor completion is most often accomplished via low-rank sparse tensor factorization, a computationally expensive non-convex optimization problem which has only recently been studied in the context of parallel computing. In this work, we study three optimization algorithms that have been successfully applied to tensor completion: alternating least squares (ALS), stochastic gradient descent (SGD), and coordinate descent (CCD++). We explore opportunities for parallelism on shared- and distributed-memory systems and address challenges such as memory- and operation-efficiency, load balance, cache locality, and communication. Among our advancements are a communication-efficient CCD++ algorithm, an ALS algorithm rich in level-3 BLAS routines, and an SGD algorithm which combines stratification with asynchronous communication. Furthermore, we show that introducing randomization during ALS and CCD++ can accelerate convergence. We evaluate our parallel formulations on a variety of real datasets on a modern supercomputer and demonstrate speedups through 16384 cores. Further, these improvements reduce time-to-solution from hours to seconds on real-world datasets. We show that after our optimizations, ALS is advantageous on parallel systems of small-to-moderate scale, while both ALS and CCD++ provide the lowest time-to-solution on large-scale distributed systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Spatial and Temporal Variations in the Moment Tensor Solutions of the 2008 Wenchuan Earthquake Aftershocks and Their Tectonic Implications

Following the mainshock of the 2008 M8 Wenchuan Earthquake, there were more than 300 M L ≥ 4.0 aftershocks that occurred between 12 May 2008 and 8 September 2010. We analyzed here the broadband waveforms for these events and found 160 events with sufficient signal-to-noise levels to invert for seismic moment tensors. Considering the length of the activated fault and the distances to the recording stations, four velocity models were employed to account for variability in crustal structure. The moment tensor solutions show considerable variations with a mixture of mainly reverse and strike-slip mechanisms and a small number of normal events and ambiguous events. We analyzed the spatial and temporal distribution of the aftershocks and their mechanism types to characterize the structure and the deformation occurring in the Longmen Shan fold and thrust belt. Our results suggest that the stress is very complex at the Longmen Shan fault zone. The moment tensors have both a spatial segmentation with two major categories of the moment tensor of thrust and strike slip; and a temporal pattern that the majority of the aftershocks gradually migrated to thrust-type events. The variability of aftershock mechanisms is a strong indication of significant tectonic release and stress reorganization that activated numerous small faults in the system.

58 GEOSCIENCES↗
DOE OSTI2019

PASTA: A Parallel Sparse Tensor Algorithm Benchmark Suite

Tensor methods have gained increasingly attention from various applications, including machine learning, quantum chemistry, healthcare analytics, social network analysis, data mining, and signal processing, to name a few. Sparse tensors and their algorithms become critical to further improve the performance of these methods and enhance the interpretability of their output. This work presents a sparse tensor algorithm benchmark suite (PASTA) for single- and multi-core CPUs. To the best of our knowledge, this is the first benchmark suite for sparse tensor world. PASTA targets on: 1) helping application users to evaluate different computer systems using its representative computational workloads; 2) providing insights to better utilize existed computer architecture and systems and inspiration for the future design. This benchmark suite will be publicly released.

HPC, sparse tensor, benchmark↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
DOE OSTI2023

High-dimensional data analytics in civil engineering: A review on matrix and tensor decomposition

Recent developments in sensing and monitoring techniques have led to the generation of high-dimensional data in the field of civil engineering. High-dimensional data analytics methods have thus been developed to interpret such complex data. Among the different high-dimensional data analytics techniques, matrix and tensor decomposition methods have acquired a notable interest in the civil engineering community over the past decade. Due to their unique ability to deal with highly redundant and correlated data, these methods are establishing themselves as promising and efficient tools to analyze high-dimensional data in the civil engineering arena. In this paper, high-dimensional data is referred to as a data set in which the number of features is comparable or larger than the number of observations. This review paper aims to summarize the applications of matrix and tensor decomposition methods in civil engineering over the last decade. The survey begins with a general overview of matrix and tensor decomposition followed by highlighting their significance in the field. Afterward, various applications of these high-dimensional data analytics methods in civil engineering are presented, while the advantages offered by these methods are discussed. Lastly, challenges and potential research avenues for employing matrix and tensor decomposition and future emerging trends for their novel use are highlighted.

42 ENGINEERING↗
DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗