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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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DOE OSTI2015

Batched matrix computations on hardware accelerators based on GPUs

Scientific applications require solvers that work on many small size problems that are independent from each other. At the same time, the high-end hardware evolves rapidly and becomes ever more throughput-oriented and thus there is an increasing need for an effective approach to develop energy-efficient, high-performance codes for these small matrix problems that we call batched factorizations. The many applications that need this functionality could especially benefit from the use of GPUs, which currently are four to five times more energy efficient than multicore CPUs on important scientific workloads. This study, consequently, describes the development of the most common, one-sided factorizations, Cholesky, LU, and QR, for a set of small dense matrices. The algorithms we present together with their implementations are, by design, inherently parallel. In particular, our approach is based on representing the process as a sequence of batched BLAS routines that are executed entirely on a GPU. Importantly, this is unlike the LAPACK and the hybrid MAGMA factorization algorithms that work under drastically different assumptions of hardware design and efficiency of execution of the various computational kernels involved in the implementation. Thus, our approach is more efficient than what works for a combination of multicore CPUs and GPUs for the problems sizes of interest of the application use cases. The paradigm where upon a single chip (a GPU or a CPU) factorizes a single problem at a time is not at all efficient in our applications’ context. We illustrate all of these claims through a detailed performance analysis. With the help of profiling and tracing tools, we guide our development of batched factorizations to achieve up to two-fold speedup and three-fold better energy efficiency as compared against our highly optimized batched CPU implementations based on MKL library. Finally, the tested system featured two sockets of Intel Sandy Bridge CPUs and we compared with a batched LU factorizations featured in the CUBLAS library for GPUs, we achieve as high as 2.5× speedup on the NVIDIA K40 GPU.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

An Asynchronous Task-based Fan-Both Sparse Cholesky Solver

Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix factorizations are sometimes needed to ensure accurate solutions. For example, accurate solution of sparse linear systems is needed in shift-invert Lanczos to compute interior eigenvalues. The performance and resource usage of sparse matrix factorizations are critical to time-to-solution and maximum problem size solvable on a given platform. In many applications, the coefficient matrices are symmetric, and exploiting symmetry will reduce both the amount of work and storage cost required for factorization. When the factorization is performed on large-scale distributed memory platforms, communication cost is critical to the performance of the algorithm. At the same time, network topologies have become increasingly complex, so that modern platforms exhibit a high level of performance variability. This makes scheduling of computations an intricate and performance-critical task. In this paper, we investigate the use of an asynchronous task paradigm, one-sided communication and dynamic scheduling in implementing sparse Cholesky factorization (symPACK) on large-scale distributed memory platforms. Our solver symPACK relies on efficient and flexible communication primitives provided by the UPC++ library. Performance evaluation shows good scalability and that symPACK outperforms state-of-the-art parallel distributed memory factorization packages, validating our approach on practical cases.

Jacquelin, Mathias↗

DOE OSTI2022

Report on PTT Imaging of Defects in AM Metallic Materials-Part 2

36 MATERIALS SCIENCE↗

DOE OSTI2022

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components (Final Technical Report)

Metal Additive Manufacturing (AM) is a promising method for cost-efficient fabrication of complex shape structures for applications in harsh environment, such as in a nuclear reactor. However, internal defects (pores) occur in high-strength AM alloys, which are manufactured with Laser Powder Bed Fusion (LPBF) AM method. Pulsed Infrared Thermography (PIT) is an efficient nondestructive evaluation (NDE) method to examine actual structures, because this method offers one-sided non-contact measurements, and fast processing of large sample areas. However, imaging of material defects, particularly defects with sizes at microscopic level, is challenging. In this report, we benchmark the performance of several Unsupervised Learning (UL) algorithms designed to enhance imaging of microscopic defects in metals with PIT. UL aims to learn the latent principal patterns (dictionaries) in PIT data to detect defects with minimal human supervision. Performance of Independent Component Analysis (ICA), Sparse Coding (SC), Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA) was compared using F-score, UL model training time and defects reconstruction time. We obtained the average F-score of 0.75, and a highest F-score of 0.89 for the EFA algorithm. Overall, EFA outperforms other UL algorithms considered in this study. In another approach, we investigate Thermal Tomography (TT), which is a computational method for reconstruction of depth profile of internal material defects from PIT nondestructive evaluation (NDE). TT algorithm obtains depth reconstructions of thermal effusivity, which has been shown to provide visualization of subsurface internals defects in metals. In many applications, one needs to determine the defect shape and orientation from reconstructed effusivity images. Interpretation of TT images is non-trivial because of blurring, which increases with depth due to heat diffusion-based nature of image formation. We have developed a deep learning convolutional neural network (CNN) to classify size and orientation of subsurface material defects in TT images. CNN was trained with TT images produced with computer simulations of 2D metallic structures (thin plates) containing elliptical subsurface voids. Performance of CNN was investigated using test TT images developed with computer simulations of plates containing elliptical defects, and defects with shape imported from scanning electron microscopy (SEM) images. CNN demonstrated the ability to classify radii and angular orientation of elliptical defects in previously unseen test TT images. We have also demonstrated that CNN trained on TT images of elliptical defects is capable of classifying shape and orientation of irregular defects. Training the CNN on irregular defect shapes instead of on elliptical shapes would make the resulting classifications more descriptive of actual defect shapes. However, this requires a much higher volume of SEM images of material defects, which are difficult to obtain because of random occurrence of defects in LPBF. To address this challenge, we developed a generative adversarial network (GAN) to augment the existing dataset of SEM defect images. The GAN model is demonstrated to create novel yet realistic defect shapes that can be used as input for simulated PTT images to train CNN. We also investigate several approaches based on Gaussian Random Circle and Bezier Curves for constructing parametric models of irregular-shape defects.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗