Approximate methods for electronic structure, implemented in sophisticated computer codes and married to ever-more powerful computing platforms, have become invaluable in chemistry and materials science. The maturing and consolidation of quantum chemistry codes since the 1980s, based upon explicitly correlated electronic wave functions, has made them a staple of modern molecular chemistry. Here, the impact of first principles electronic structure in physics and materials science had lagged owing to the extra formal and computational demands of bulk calculations.
We investigate a novel application of deep neural networks to modeling of errors in prediction of surface pressure fluctuations beneath a compressible, turbulent flow. In this context, the truth solution is given by Direct Numerical Simulation (DNS) data, while the predictive model is a wall-modeled Large Eddy Simulation (LES). The neural network provides a means to map relevant statistical flow-features within the LES solution to errors in prediction of wall pressure spectra. We simulate a number of flat plate turbulent boundary layers using both DNS and wall-modeled LES to build up a database with which to train the neural network. We then apply machine learning techniques to develop an optimized neural network model for the error in terms of relevant flow features.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Mkrtchyan, Vahan; Parekh, Ojas D.; Segev, Danny; Subramani, K.
Motivated by applications in risk management of computational systems, we focus our attention on a special case of the partial vertex cover problem, where the underlying graph is assumed to be a tree. Here, we consider four possible versions of this setting, depending on whether vertices and edges are weighted or not. Two of these versions, where edges are assumed to be unweighted, are known to be polynomial-time solvable. However, the computational complexity of this problem with weighted edges, and possibly with weighted vertices, has not been determined yet. The main contribution of this paper is to resolve these questions by fully characterizing which variants of partial vertex cover remain intractable in trees, and which can be efficiently solved. In particular, we propose a pseudo-polynomial DP-based algorithm for the most general case of having weights on both edges and vertices, which is proven to be NP-hard. This algorithm provides a polynomialtime solution method when weights are limited to edges, and combined with additional scaling ideas, leads to an FPTAS for the general case. A secondary contribution of this work is to propose a novel way of using centroid decompositions in trees, which could be useful in other settings as well.
The Rim-to-Rim Wearables At The Canyon for Health (R2R WATCH) study examines metrics recordable on commercial off the shelf (COTS) devices that are most relevant and reliable for the earliest possible indication of a health or performance decline. This is accomplished through collaboration between Sandia National Laboratories (SNL) and The University of New Mexico (UNM) where the two organizations team up to collect physiological, cognitive, and biological markers from volunteer hikers who attempt the Rim-to-Rim (R2R) hike at the Grand Canyon. Three forms of data are collected as hikers travel from rim to rim: physiological data through wearable devices, cognitive data through a cognitive task taken every 3 hours, and blood samples obtained before and after completing the hike. Data is collected from both civilian and warfighter hikers. Once the data is obtained, it is analyzed to understand the effectiveness of each COTS device and the validity of the data collected. We also aim to identify which physiological and cognitive phenomena collected by wearable devices are the most relatable to overall health and task performance in extreme environments, and of these ascertain which markers provide the earliest yet reliable indication of health decline. Finally, we analyze the data for significant differences between civilians’ and warfighters’ markers and the relationship to performance. This is a study funded by the Defense Threat Reduction Agency (DTRA, Project CB10359) and the University of New Mexico (The main portion of the R2R WATCH study is funded by DTRA. UNM is currently funding all activities related to bloodwork. DTRA, Project CB10359; SAND2017-1872 C). This paper describes the experimental design and methodology for the first year of the R2R WATCH project.
Emerging novel architectures for shared memory parallel computing are incorporating increasingly creative innovations to deliver higher memory performance. A notable exemplar of this phenomenon is the Multi-Channel DRAM (MCDRAM) that is included in the Intel® XeonPhi™ processors. In this paper, we examine techniques to use OpenMP to exploit the high bandwidth of MCDRAM by staging data. In particular, we implement double buffering using OpenMP sections and tasks to explicitly manage movement of data into MCDRAM. We compare our double-buffered approach to a non-buffered implementation and to Intel’s cache mode, in which the system manages the MCDRAM as a transparent cache. We also demonstrate the sensitivity of performance to parameters such as dataset size and the distribution of threads between compute and copy operations.
Many engineering design problems can be formulated in the framework of partial differential equation (PDE) constrained optimization. The discretization of a PDE leads to multiple levels of resolution with varying degrees of numerical solution accuracy. Coarse discretizations require less computational time at the expense of increased error. Often there are also reduced fidelity models available, with simplifications to the physics models that are computationally easier to solve. This research develops an up to second-order consistent multilevel-multifidelity (MLMF) optimization scheme that exploits the reduced cost resulting from coarse discretization and reduced fidelity to more efficiently converge to the optimum of a fine-grid high-fidelity problem. This scheme distinguishes multilevel approaches applied to discretizations from multifidelity approaches applied to model forms, and navigates both hierarchies to accelerate convergence. Additive, multiplicative, or a combination of both corrections can be applied to the sub-problems to enforce up to second-order consistency with the fine-grid high-fidelity results. The MLMF optimization algorithm is a wrapper around a subproblem optimization solver, and the MLMF scheme is provably convergent if the subproblem optimizer is provably convergent. Heuristics are developed for efficiently tuning optimization tolerances and iterations at each level and fidelity based on relative solution cost. Accelerated convergence is demonstrated for a simple one-dimensional problem and aerodynamic shape optimization of a transonic airfoil.
Fault-tolerance poses a major challenge for future large-scale systems. Active research into coordinated, uncoordinated, and hybrid checkpointing systems has explored how the introduction of asynchrony can address anticipated scalability issues. While fully uncoordinated approaches have been shown to have significant delays, the degree of sychronization required to keep overheads low has not yet been significantly addressed. In this paper, we use a simulation-based approach to show the impact of synchronization on local checkpoint activity. Specifically, we show the degree of synchronization needed to keep the impacts of local checkpointing low is attainable with current technology for a number of key production HPC workloads. Our work provides a critical analysis and comparison of synchronization and local checkpointing. This enables users and system administrators to fine-tune the checkpointing scheme to the application and system characteristics available.
Debenedictis, Erik; Badaroglu, Mustafa; Chen, An; Conte, Thomas M.; Gargini, Paolo
Rather than continue the expensive and time-consuming quest for transistor replacement, the authors argue that 3D chips coupled with new computer architectures can keep Moore's law on its traditional scaling path.
Researchers are now considering alternatives to the von Neumann computer architecture as a way to improve performance. The current approach of simulating benchmark applications favors continued use of the von Neumann architecture, but architects can help overcome this bias.
The dentate gyrus forms a critical link between the entorhinal cortex and CA3 by providing a sparse version of the signal. Concurrent with this increase in sparsity, a widely accepted theory suggests the dentate gyrus performs pattern separation-similar inputs yield decorrelated outputs. Although an active region of study and theory, few logically rigorous arguments detail the dentate gyrus's (DG) coding.We suggest a theoretically tractable, combinatorial model for this action. The model provides formal methods for a highly redundant, arbitrarily sparse, and decorrelated output signal. To explore the value of this model framework, we assess how suitable it is for two notable aspects of DG coding: how it can handle the highly structured grid cell representation in the input entorhinal cortex region and the presence of adult neurogenesis, which has been proposed to produce a heterogeneous code in the DG.We find tailoring themodel to grid cell input yields expansion parameters consistent with the literature. In addition, the heterogeneous coding reflects activity gradation observed experimentally. Finally,we connect this approach with more conventional binary threshold neural circuit models via a formal embedding.
We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points xi. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains O(hm) convergence in both L2- and H1-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.
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 14 ×, 45 ×, and 27 × 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.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress towards optimal engine designs requires both accurate flow simulations as well as uncertainty quantification (UQ). However, performing UQ for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. We address these difficulties by combining UQ algorithms and numerical methods to the large eddy simulation of the HIFiRE scramjet configuration. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, helping reduce the stochastic dimension of the problem and discover sparse representations. Second, as models of different fidelity are available and inevitably used in the overall UQ assessment, a framework for quantifying and propagating the uncertainty due to model error is introduced. These methods are demonstrated on a non-reacting scramjet unit problem with parameter space up to 24 dimensions, using 2D and 3D geometries with static and dynamic treatments of the turbulence subgrid model.
We establish an atomistic view of the high- and low-temperature phases of iron/steel as well as some elements of the phase transition between these phases on cooling. In particular we examine the 4 most common orientation relationships between the high temperature austenite and low-temperature ferrite phases seen in experiment. With a thorough understanding of these relationships we are prepared to set up various atomistic simulations, using techniques such as Density Functional Theory and Molecular Dynamics, to further study the phase transition, in particular, quantities needed for Phase Field Modeling, such as the free energies of bulk phases and the phase transition front propagation velocity.