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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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks↗
DOE OSTI2016

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.

2.5D algorithms↗
DOE OSTI2020

Stochastic Gradients for Large-Scale Tensor Decomposition

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of loss functions such as Bernoulli loss for binary data or Huber loss for robust estimation. Here, the stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor times Khatri--Rao product tensor kernel. For dense tensors, we simply use uniform sampling. For sparse tensors, we propose two types of stratified sampling that give precedence to sampling nonzeros. Numerical results demonstrate the advantages of the proposed approach and its scalability to large-scale problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Computing the Properties of Hadrons, Nuclei, and Nuclear Matter from Quantum Chromodynamics, UNC-CH Final Report.

This is the final technical report for the UNC-CH component of a SciDAC3 project. This project served to coordinate the software development effort which the nuclear physics lattice QCD community is developing to ensure that lattice calculations can make optimal use of forthcoming leadership-class and dedicated hardware, including those of the national laboratories, and prepares for the exploitation of future computational resources in the exascale era. The project developed and optimized simulation software for lattice QCD calculations on leadership class computers and on GPUaccelerated heterogeneous architectures. The participating team at multiple instritutions improved and extended software libraries (Chroma, CPS, MILC, QLUA, QPhiX, QDP++, QDP-jit) by providing interfaces for heterogeneous computing environments and through the optimization of gauge field evolution algorithms and sparse matrix inverters. The former includes the development of new multi-time scale integrators and the latter focused on the development of new multi-grid and domain decomposition inverters for several QCD fermion discretization schemes. The sub-project at the University of North Carolina worked towards the development a domain specific language for lattice QCD computations with the express purpose of generating code with uncompromised performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

DECT-MULTRA: Dual-Energy CT Image Decomposition With Learned Mixed Material Models and Efficient Clustering

Dual-energy computed tomography (DECT) imaging plays an important role in advanced imaging applications due to its material decomposition capability. Image-domain decomposition operates directly on CT images using linear matrix inversion, but the decomposed material images can be severely degraded by noise and artifacts. This paper proposes a new method dubbed DECT-MULTRA for image-domain DECT material decomposition that combines conventional penalized weighted-least squares (PWLS) estimation with regularization based on a mixed union of learned transforms (MULTRA) model. Our proposed approach pre-learns a union of common-material sparsifying transforms from patches extracted from all the basis materials, and a union of cross-material sparsifying transforms from multi-material patches. The common-material transforms capture the common properties among different material images, while the cross-material transforms capture the cross-dependencies. The proposed PWLS formulation is optimized efficiently by alternating between an image update step and a sparse coding and clustering step, with both of these steps having closed-form solutions. The effectiveness of our method is validated with both XCAT phantom and clinical head data. The results demonstrate that our proposed method provides superior material image quality and decomposition accuracy compared to other competing methods.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

ChatMPI: LLM-Driven MPI Code Generation for HPC Workloads

The Message Passing Interface (MPI) standard plays a crucial role in enabling scientific applications for parallel computing and is an essential component in high-performance computing (HPC). However, implementing MPI code manually—especially applying a proper domain decomposition and communication pattern—is a challenging and error-prone task. We present ChatMPI, an AI assistant for MPI parallelization of sequential C codes. In our analysis, we focus on testing six essential HPC workloads, which are based on Basic Linear Algebra Subprograms levels 1, 2, and 3 as well as sparse, stencil, and iterative operations. We analyze the process of creating ChatMPI by using the ChatHPC library. This lightweight large language model (LLM)–based infrastructure enables HPC experts to efficiently create and supervise trustworthy AI capabilities for critical HPC software tasks. We study the data required for training (fine-tuning) ChatMPI to generate parallel codes that not only use MPI syntax correctly but also apply HPC techniques to reduce memory communication and maximize performance by using proper work decomposition. With a relatively small training dataset composed of a few dozen prompts and fewer than 15 minutes of fine-tuning on one node equipped with two NVIDIA H100 GPUs, ChatMPI elevates trustworthiness for MPI code generation of current LLMs (e.g., Code Llama, ChatGPT-4o and ChatGPT 5). Additionally, we evaluate the performance of the MPI codes generated by ChatMPI in comparison with the ones generated by ChatGPT-4o and ChatGPT-5. The codes generated by ChatMPI provide up to a 4 × boost in performance by using better problem decomposition, communication patterns, and HPC techniques (e.g., communication avoiding).

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗
DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Monitoring Surface Phenomena Created by an Underground Chemical Explosion Using Fully Polarimetric VideoSAR

Sandia National Laboratories flew its Facility for Advanced RF and Algorithm Development X-Band (9.6-GHz center frequency), fully polarimetric synthetic aperture radar (PolSAR) in VideoSAR mode to collect complex-valued SAR imagery before, during, and after the sixth Source Physics Experiment's (SPE-6) underground explosion. The VideoSAR products generated from the data sets include "movies'' of single- and quad-polarization coherence maps, magnitude imagery, and polarimetric decompositions. Residual defocus, due to platform motion during data acquisition, was corrected with a digital elevation model-based autofocus algorithm. We generated and exploited the VideoSAR image products to characterize the surface movement effects caused by the underground explosion. Unlike seismic sensors, which measure local area seismic waves using sparse spacing and subterranean positioning, these VideoSAR products captured high-spatial resolution, 2-D, time-varying surface movement. The results from the fifth SPE (SPE-5) used single-polarimetric VideoSAR data. In this paper, we present single-polarimetric and fully polarimetric VideoSAR results while monitoring the SPE-6 underground chemical explosion. We show that fully polarimetric VideoSAR imaging provides a unique, coherent, time-varying measure of the surface expression of the SPE-6 underground chemical explosion. As a result, we include new surface characterization results from the measured PolSAR SPE-6 data via H/A/α polarimetric decomposition.

47 OTHER INSTRUMENTATION↗
DOE OSTI2012

High performance radiation transport simulations: Preparing for TITAN

In this paper we describe the Denovo code system. Denovo solves the six-dimensional, steady-state, linear Boltzmann transport equation, of central importance to nuclear technology applications such as reactor core analysis (neutronics), radiation shielding, nuclear forensics and radiation detection. The code features multiple spatial differencing schemes, state-of-the-art linear solvers, the Koch-Baker-Alcouffe (KBA) parallel-wavefront sweep algorithm for inverting the transport operator, a new multilevel energy decomposition method scaling to hundreds of thousands of processing cores, and a modern, novel code architecture that supports straightforward integration of new features. In this paper we discuss the performance of Denovo on the 20+ petaflop ORNL GPU-based system, Titan. We describe algorithms and techniques used to exploit the capabilities of Titan's heterogeneous compute node architecture and the challenges of obtaining good parallel performance for this sparse hyperbolic PDE solver containing inherently sequential computations. Numerical results demonstrating Denovo performance on early Titan hardware are presented.

Baker, C.↗
NASA NTRS2008

A Data Type for Efficient Representation of Other Data Types

A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.

James, Mark↗
DOE OSTI2016

THE NUCLEAR ACTIVITIES OF NEARBY S0 GALAXIES

We present a study of nuclear activities in nearby S0 galaxies. After cross-matching the Sloan Digital Sky Survey Data Release 7 with the Third Reference Catalog of Bright Galaxies (RC3) and visually checking the SDSS images, we derive a sample of 583 S0 galaxies with the central spectrophotometric information. In order to separate nebular emission lines from the underlying stellar contribution, we fit the stellar population model to the SDSS spectra of these S0 galaxies. According to the BPT diagram, we find that 8% of S0 galaxies show central star-forming activity, while the fractions of Seyfert, Composite, and low-ionization nuclear emission-line regions (LINERs) are 2%, 8%, and 21.4%, respectively. We also find that star-forming S0s have the lowest stellar masses, over one magnitude lower than the others, and that the active S0s are mainly located in the sparse environment, while the normal S0s are located in the dense environment, which might suggest that the environment plays an important role in quenching star formation and/or AGN activity in S0 galaxies. By performing bulge-disk decomposition of 45 star-forming S0s in g - and r -bands with the 2D fitting software Galfit, as well as exploiting the catalog of 2D photometric decompositions of Meert et al., we find that the bulges of approximately one-third of star-forming S0 galaxies (16/45) are bluer than their disks, while for other types of S0s the bulge and disk components show similar color distributions. Besides, the Sérsic index of most star-forming S0s bulges is less than two, while for normal S0s, it is between two and six.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

Abstract There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm.

Pawar, Suraj↗
DOE OSTI2026

Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction Method

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of the Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals N, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ∼1,200 orbitals) show that (a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; (b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity─some blocks nearly full rank and many low rank, naturally motivates the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. In conclusion, we demonstrate that the mixed scheme yields cubic wall-time scaling with favorable prefactors and preserves AFQMC accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Sparsity of Radiating Characteristic Modes on Infinite Periodic Structures

Characteristic modes on infinite periodic structures are studied using spectral dyadic Green’s functions. This formulation demonstrates that, in contrast to the modal analysis of finite structures, the number of radiating characteristic modes is limited by unit cell size and incident wave vector (i.e., scan angle or phase shift per unit cell). Here, the reflection tensor is decomposed into modal contributions from radiating modes, indicating that characteristic modes are a predictably sparse basis in which to study reflection phenomena.

42 ENGINEERING↗
DOE OSTI2016

Reducing Computation and Communication in Scientific Computing: Connecting Theory to Practice.

This report summarizes the work produced as part of a Truman Fellowship appointment and its associated LDRD project. The overall goal of the project was to develop better algorithms and implementations for key computational kernels within the field of scientific computing by designing them to be communication efficient, moving as little data as possible. The primary problem of interest was dense matrix multiplication; other computations that were addressed include sparse matrix-matrix multiplication, QR factorization, solving symmetric linear systems, and the symmetric eigendecomposition. The project also involved the study of computations at the intersection of scientific computing and data analysis, including nonnegative matrix factorization for discovering latent factors, Tucker tensor decomposition for data compression, and sampling methods for similarity search.

97 MATHEMATICS AND COMPUTING↗