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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 OSTI2025

Accelerating GNNs on GPU Sparse Tensor Cores through N:M Sparsity-Oriented Graph Reordering

Recent advancements in GPU hardware support have introduced the capability to leverage N:M sparse patterns for substantial performance gains. Graphs in Graph Neural Networks (GNNs) are typically sparse, but the sparsity is often irregular, not conforming to such sparse patterns. In this paper, we propose a novel graph reordering algorithm, the first of its kind, to reshape irregular graph data into the N:M structured sparse pattern at the tile level, allowing linear-algebra-based graph operations in GNNs to benefit from the N:M sparse hardware. The optimization is lossless, maintaining the accuracy of GNN. It can remove 98-100\% violations of the N:M sparse patterns at the vector level, and increase the proportion of conforming graphs in SuiteSparse collection from 5-9\% to 88.7-93.5\%. On A100 GPUs, the optimization accelerates Sparse Matrix Matrix (SpMM) by up to 43X (2.3X -- 7.5X on average) and speeds up the key graph operations in GNNs on real graphs by as much as 8.6X (3.5X on average).

artificial intelligence, graph neural networks↗
DOE OSTI2024

Accelerated Constrained Sparse Tensor Factorization on Massively Parallel Architectures

This study presents the first constrained sparse tensor factorization (cSTF) framework that optimizes and fully offloads computation to massively parallel GPU architectures, and the first performance characterization of cSTF on GPU architectures. In contrast to prior work on tensor factorization, where the matricized tensor times Khatri-Rao product (MTTKRP) is the primary performance bottleneck, our systematic analysis of the cSTF algorithm on GPUs reveals that adding constraints creates an additional bottleneck in the update operation for many real-world sparse tensors. While executing the update operation on the GPU brings significant speedup over its CPU counterpart, it remains a significant bottleneck. To further accelerate the update operation, we propose cuADMM, a new update algorithm that leverages algorithmic and code optimization strategies to minimize both computation and data movement on GPUs. As a result, our framework delivers significantly improved performance compared to prior state-of-the-art. On 10 real-world sparse tensors, our framework achieves geometric mean speedup of 5.1 × (max 41.59 ×) and 7.01 × (max 58.05 ×) on the NIVIDA A100 and H100 GPUs, respectively, over the state-of-the-art SPLATT library running on a 26-core Intel Ice Lake Xeon CPU.

Soh, Yongseok↗
DOE OSTI2024

Computing Sparse Tensor Decompositions via Chapel and C++/MPI Interoperability without Intermediate I/O

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions that provide use of shared mapped memory tensor data for a particular C++ tensor decomposition tool called GentenMPI. We then demonstrate our approach on several real-world datasets, providing timing results that illustrate minimal overhead incurred using this approach. Finally, we extend our work to improve memory usage and provide convenient random access to sparse shared mapped memory tensor elements in Chapel, while still being capable of leveraging high performance implementations of tensor algorithms in C++.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Flexible Forwarding Scheme to Improve Latency-Bound Irregular P2P Communication in MPI

We propose an algorithm to efficiently perform latency-bound communication scenarios that consist of many small messages. In these parallel scenarios, processes typically pass around a lot of small-sized messages of a few KBs of size. Performing communication operations with P2P MPI routines or collective MPI routines (including neighborhood collectives) in such scenarios may not always yield the optimal results and may not resolve the latency bottleneck. To this end, we develop a regular structure called virtual process topology (VPT) on which the messages can be communicated in a structured and controlled manner. Using parameters of this topology, one can tune the rate of aggression in tackling the latency costs. We demonstrate that our communication algorithm is preferable to MPI P2P and collective routines for latency-bound communication and it can easily be adapted only by replacing calls to MPI routines in a parallel application. We show how to adapt existing topology-aware mapping heuristics to address the volume overhead due to communicating messages on the VPT. Moreover, we propose a novel swap-based mapping heuristic to address this overhead by optimizing the maximum volume handled by a process. Experiments on synthetic communication graphs as well as real-world applications such as parallel Canonical Polyadic sparse tensor decomposition and parallel sparse matrix-dense matrix multiplication show that our approach is a powerful way of overcoming the bottlenecks posed by sparse and latency-bound irregular communication.

communication algorithm↗
DOE OSTI2025

Enabling Efficient Sparse Computations using Linear Algebra Aware Compilers

This project developed the LAPIS compiler framework, built on the Multilevel Intermediate Representation (MLIR), to optimize sparse linear algebra operations and support performance portability across diverse architectures. The main innovation of LAPIS is the Kokkos dialect, which allows for lowering codes from a high productivity language to different architectures in an elegant way. The dialect also allows the conversion of lower-level MLIR code to C++ Kokkos code, facilitating the integration of scientific machine learning (SciML) models into applications. To extend LAPIS for distributed memory architectures, a new partition dialect was created to manage the distribution of sparse tensors and express communication patterns for sparse linear algebra operations. This dialect also supports the distributed execution of operators and includes algorithmic optimizations to minimize communication to improve performance. The project also demonstrates that MLIR can enable effective linear algebra-level optimizations, improving performance on different GPUs for both sparse and dense linear algebra kernels. Key applications of LAPIS include sparse linear algebra and graph kernels, TenSQL, a relational database management solution built on GraphBLAS, and the development of subgraph isomorphism and monomorphism kernels, showcasing performance portability. In summary, the LAPIS framework supports productivity, performance, portability, and distributed memory execution, while also enabling linear algebra-level optimizations that are challenging in traditional programming languages, with successful applications ranging from simple sparse linear algebra to complex graph kernels.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

sparsett

Python module for working with sparse tensors.

Lilly, Jeremy [Los Alamos National Lab]↗
NASA NTRS2016

On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields

This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.

Uncertainty↗
NASA NTRSDate not supplied

Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations

The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.

quantum computing↗
DOE OSTI2023

Sparse Symmetric Format for Tucker Decomposition

Tensor-based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $\underline{S}$ parse $\underline{S}$ ymmetric $\underline{T}$ ensor $\underline{T}$ imes $\underline{S}$ ame $\underline{M}$ atrix $\underline{c}$ hain (S 3 TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S 3 TTM c operation. We theoretically establish that S 3 TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

42 ENGINEERING↗
DOE OSTI2025

SymProp: Scaling Sparse Symmetric Tucker Decomposition via Symmetry Propagation

Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain (S3 TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core (S3 TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to 50.9× speedup over SPLATT and up to 360.8× over Compressed Sparse Symmetric (CSS) format on the S3 TTMc operation. Moreover, our S3 TTMc and S3 TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a 33.6× speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Li, Zecheng [North Carolina State University]↗
NASA NTRS1994

Tensor-GMRES method for large sparse systems of nonlinear equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Feng, Dan↗
DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗
DOE OSTI2023

Toward Global Regional Seismic Moment Tensor Inversion with Three-Dimensional Earth Models for Nuclear Explosion Monitoring with Sparse Networks: Demonstration of Reciprocity for Strain Greens Tensor Database Simulation with Salvus

Seismic source characterization is an essential function of global nuclear explosion monitoring (NEM). While large events (roughly with moment magnitude, M w , greater than 5.0) can often be easily detected, located and identified with high signal-to-noise ratios at teleseismic distances (> 20°), trends in NEM research require confident source characterization at much lower magnitudes (say down to 3.0) and exploitation of sparse observations (from only a few stations) at regional distance (< 20°). Regional distance waveform inversion to characterize sources is now widely used and effective (e.g. Ford et al., 2009; Alvizuri and Tape, 2018; Alvizuri et al., 2018; Chiang et al., 2018; Ford et al., 2022). These methods obtain the magnitude, depth and seismic moment tensor, which represents the forces that excited the observed seismic waves (slip on an earthquake fault, explosion, collapse or a combination of various forces). Common to many problems in seismology, the isolation of the source 2 properties requires removal of path propagation effects that waves experience while traveling through the three-dimensional (3D) Earth (the structure exists due to different rock types, material properties, temperature and tectonic processes).

58 GEOSCIENCES↗
DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

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

Beyond PCA: Additional Dimension Reduction Techniques to Consider in the Development of Climate Fingerprints

Abstract Dimension reduction techniques are an essential part of the climate analyst’s toolkit. Due to the enormous scale of climate data, dimension reduction methods are used to identify major patterns of variability within climate dynamics, to create compelling and informative visualizations, and to quantify major named modes such as El Niño–Southern Oscillation. Principal components analysis (PCA), also known as the method of empirical orthogonal functions (EOFs), is the most commonly used form of dimension reduction, characterized by a remarkable confluence of attractive mathematical, statistical, and computational properties. Despite its ubiquity, PCA suffers from several difficulties relevant to climate science: high computational burden with large datasets, decreased statistical accuracy in high dimensions, and difficulties comparing across multiple datasets. In this paper, we introduce several variants of PCA that are likely to be of use in climate sciences and address these problems. Specifically, we introduce non-negative , sparse , and tensor PCA and demonstrate how each approach provides superior pattern recognition in climate data. We also discuss approaches to comparing PCA-family results within and across datasets in a domain-relevant manner. We demonstrate these approaches through an analysis of several runs of the E3SM climate model from 1991 to 1995, focusing on the simulated response to the Mt. Pinatubo eruption; our findings are consistent with a recently identified stratospheric warming fingerprint associated with this type of stratospheric aerosol injection.

Weylandt, Michael↗