We propose a porous materials analysis pipeline using persistent homology. We rst compute persistent homology of binarized 3D images of sampled material subvolumes. For each image we compute sets of homology intervals, which are represented as summary graphics called persistence diagrams. We convert persistence diagrams into image vectors in order to analyze the similarity of the homology of the material images using the mature tools for image analysis. Each image is treated as a vector and we compute its principal components to extract features. We t a statistical model using the loadings of principal components to estimate material porosity, permeability, anisotropy, and tortuosity. We also propose an adaptive version of the structural similarity index (SSIM), a similarity metric for images, as a measure to determine the statistical representative elementary volumes (sREV) for persistence homology. Thus we provide a capability for making a statistical inference of the uid ow and transport properties of porous materials based on their geometry and connectivity.
The FY18Q1 milestone of the ECP/VTK-m project includes the implementation of a multiblock data set, the completion of a gradients filtering operation, and the release of version 1.1 of the VTK-m software. With the completion of this milestone, the new multiblock data set allows us to iteratively schedule algorithms on composite data structures such as assemblies or hierarchies like AMR. The new gradient algorithms approximate derivatives of fields in 3D structures with finite differences. Finally, the release of VTK-m version 1.1 tags a stable release of the software that can more easily be incorporated into external projects.
We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.
Simulating HPC systems is a difficult task and the emergence of “Beyond CMOS” architectures and execution models will increase that difficulty. This document presents a “tutorial” on some of the simulation challenges faced by conventional and non-conventional architectures (Section 1) and goals and requirements for simulating Beyond CMOS systems (Section 2). These provide background for proposed short- and long-term roadmaps for simulation efforts at Sandia (Sections 3 and 4). Additionally, a brief explanation of a proof-of-concept integration of a Beyond CMOS architectural simulator is presented (Section 2.3).
Conventional wisdom in the spacecraft domain is that on-orbit computation is expensive, and thus, information is traditionally funneled to the ground as directly as possible. The explosion of information due to larger sensors, the advancements of Moore's law, and other considerations lead us to revisit this practice. In this article, we consider the trade-off between computation, storage, and transmission, viewed as an energy minimization problem.
Unlike general purpose computer architectures that are comprised of complex processor cores and sequential computation, the brain is innately parallel and contains highly complex connections between computational units (neurons). Key to the architecture of the brain is a functionality enabled by the combined effect of spiking communication and sparse connectivity with unique variable efficacies and temporal latencies. Utilizing these neuroscience principles, we have developed the Spiking Temporal Processing Unit (STPU) architecture which is well-suited for areas such as pattern recognition and natural language processing. In this paper, we formally describe the STPU, implement the STPU on a field programmable gate array, and show measured performance data.
Most existing concepts for hardware implementation of reversible computing invoke an adiabatic computing paradigm, in which individual degrees of freedom (e.g., node voltages) are synchronously transformed under the influence of externallysupplied driving signals. But distributing these "power/clock" signals to all gates within a design while efficiently recovering their energy is difficult. Can we reduce clocking overhead using a ballistic approach, wherein data signals self-propagating between devices drive most state transitions? Traditional concepts of ballistic computing, such as the classic Billiard-Ball Model, typically rely on a precise synchronization of interacting signals, which can fail due to exponential amplification of timing differences when signals interact. In this paper, we develop a general model of Asynchronous Ballistic Reversible Computing (ABRC) that aims to address these problems by eliminating the requirement for precise synchronization between signals. Asynchronous reversible devices in this model are isomorphic to a restricted set of Mealy finite-state machines. We explore ABRC devices having up to 3 bidirectional I/O terminals and up to 2 internal states, identifying a simple pair of such devices that comprises a computationally universal set of primitives. We also briefly discuss how ABRC might be implemented using single flux quanta in superconducting circuits.
Most existing concepts for hardware implementation of reversible computing invoke an adiabatic computing paradigm, in which individual degrees of freedom (e.g., node voltages) are synchronously transformed under the influence of externallysupplied driving signals. But distributing these "power/clock" signals to all gates within a design while efficiently recovering their energy is difficult. Can we reduce clocking overhead using a ballistic approach, wherein data signals self-propagating between devices drive most state transitions? Traditional concepts of ballistic computing, such as the classic Billiard-Ball Model, typically rely on a precise synchronization of interacting signals, which can fail due to exponential amplification of timing differences when signals interact. In this paper, we develop a general model of Asynchronous Ballistic Reversible Computing (ABRC) that aims to address these problems by eliminating the requirement for precise synchronization between signals. Asynchronous reversible devices in this model are isomorphic to a restricted set of Mealy finite-state machines. We explore ABRC devices having up to 3 bidirectional I/O terminals and up to 2 internal states, identifying a simple pair of such devices that comprises a computationally universal set of primitives. We also briefly discuss how ABRC might be implemented using single flux quanta in superconducting circuits.
Proceedings of LLVM-HPC 2017: 4th Workshop on the LLVM Compiler Infrastructure in HPC - Held in conjunction with SC 2017: The International Conference for High Performance Computing, Networking, Storage and Analysis
Optimizing compilers for task-level parallelism are still in their infancy. This work explores a compiler front end that translates OpenMP tasking semantics to Tapir, an extension to LLVM IR that represents fork-join parallelism. This enables analyses and optimizations that were previously inaccessible to OpenMP codes, as well as the ability to target additional runtimes at code generation. Using a Cilk runtime back end, we compare results to existing OpenMP implementations. Initial performance results for the Barcelona OpenMP task suite show performance improvements over existing implementations.
Proceedings of PDSW-DISCS 2017 - 2nd Joint International Workshop on Parallel Data Storage and Data Intensive Scalable Computing Systems - Held in conjunction with SC 2017: The International Conference for High Performance Computing, Networking, Storage and Analysis
Significant challenges exist in the efficient retrieval of data from extreme-scale simulations. An important and evolving method of addressing these challenges is application-level metadata management. Historically, HDF5 and NetCDF have eased data retrieval by offering rudimentary attribute capabilities that provide basic metadata. ADIOS simplified data retrieval by utilizing metadata for each process' data. EMPRESS provides a simple example of the next step in this evolution by integrating per-process metadata with the storage system itself, making it more broadly useful than single file or application formats. Additionally, it allows for more robust and customizable metadata.
Many applications, such as PDE based simulations and machine learning, apply BLAS/LAPACK routines to large groups of small matrices. While existing batched BLAS APIs provide meaningful speedup for this problem type, a non-canonical data layout enabling cross-matrix vectorization may provide further significant speedup. In this paper, we propose a new compact data layout that interleaves matrices in blocks according to the SIMD vector length. We combine this compact data layout with a new interface to BLAS/LAPACK routines that can be used within a hierarchical parallel application. Our layout provides up to 14x, 45x, and 27x speedup against OpenMP loops around optimized DGEMM, DTRSM and DGETRF kernels, respectively, on the Intel Knights Landing architecture. We discuss the compact batched BLAS/LAPACK implementations in two libraries, KokkosKernels and Intel® Math Kernel Library. We demonstrate the APIs in a line solver for coupled PDEs. Finally, we present detailed performance analysis of our kernels.
Within the EXAALT project, the SNAP [1] approach is being used to develop high accuracy potentials for use in large-scale long-time molecular dynamics simulations of materials behavior. In particular, we have developed a new SNAP potential that is suitable for describing the interplay between helium atoms and vacancies in high-temperature tungsten[2]. This model is now being used to study plasma-surface interactions in nuclear fusion reactors for energy production. The high-accuracy of SNAP potentials comes at the price of increased computational cost per atom and increased computational complexity. The increased cost is mitigated by improvements in strong scaling that can be achieved using advanced algorithms [3].
When very few samples of a random quantity are available from a source distribution of unknown shape, it is usually not possible to accurately infer the exact distribution from which the data samples come. Under-estimation of important quantities such as response variance and failure probabilities can result. For many engineering purposes, including design and risk analysis, we attempt to avoid under-estimation with a strategy to conservatively estimate (bound) these types of quantities -- without being overly conservative -- when only a few samples of a random quantity are available from model predictions or replicate experiments. This report examines a class of related sparse-data uncertainty representation and inference approaches that are relatively simple, inexpensive, and effective. Tradeoffs between the methods' conservatism, reliability, and risk versus number of data samples (cost) are quantified with multi-attribute metrics use d to assess method performance for conservative estimation of two representative quantities: central 95% of response; and 10-4 probability of exceeding a response threshold in a tail of the distribution. Each method's performance is characterized with 10,000 random trials on a large number of diverse and challenging distributions. The best method and number of samples to use in a given circumstance depends on the uncertainty quantity to be estimated, the PDF character, and the desired reliability of bounding the true value. On the basis of this large data base and study, a strategy is proposed for selecting the method and number of samples for attaining reasonable credibility levels in bounding these types of quantities when sparse samples of random variables or functions are available from experiments or simulations.
We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.