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At least 793 records · Page 44

SIERRA/Aero Theory Manual - Version 5.8

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SIERRA Low Mach Module: Fuego User Manual (V.5.10)

The SIERRA Low Mach Module: Fuego, henceforth referred to as Fuego, is the key element of the ASC fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Using MPMD coupling, Scefire and Nalu handle the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

97 MATHEMATICS AND COMPUTING↗

Quantum-Hardware Focused Application Performance Benchmarks (Final Technical Report)

Quantum computers promise to transform how we do scientific calculations. In this project, we benchmark different current quantum computers for solving chemistry problems and find ways to build noise-resilient implementations. We also use the characterization techniques developed to test ion trap quantum computers.

74 ATOMIC AND MOLECULAR PHYSICS↗

Monitor support on accelerated processing device

A technique for implementing synchronization monitors on an accelerated processing device (“APD”) is provided. Work on an APD includes workgroups that include one or more wavefronts. All wavefronts of a workgroup execute on a single compute unit. A monitor is a synchronization construct that allows workgroups to stall until a particular condition is met. Responsive to all wavefronts of a workgroup executing a wait instruction, the monitor coordinator records the workgroup in an “entry queue.” The workgroup begins saving its state to a general APD memory and, when such saving is complete, the monitor coordinator moves the workgroup to a “condition queue.” When the condition specified by the wait instruction is met, the monitor coordinator moves the workgroup to a “ready queue,” and, when sufficient resources are available on a compute unit, the APD schedules the ready workgroup for execution on a compute unit.

42 ENGINEERING↗

Supercomputer-Based Ensemble Docking Drug Discovery Pipeline with Application to Covid-19

In this work, we present a supercomputer-driven pipeline for in silico drug discovery using enhanced sampling molecular dynamics (MD) and ensemble docking. Ensemble docking makes use of MD results by docking compound databases into representative protein binding-site conformations, thus taking into account the dynamic properties of the binding sites. We also describe preliminary results obtained for 24 systems involving eight proteins of the proteome of SARS-CoV-2. The MD involves temperature replica exchange enhanced sampling, making use of massively parallel supercomputing to quickly sample the configurational space of protein drug targets. Using the Summit supercomputer at the Oak Ridge National Laboratory, more than 1 ms of enhanced sampling MD can be generated per day. We have ensemble docked repurposing databases to 10 configurations of each of the 24 SARS-CoV-2 systems using AutoDock Vina. Comparison to experiment demonstrates remarkably high hit rates for the top scoring tranches of compounds identified by our ensemble approach. We also demonstrate that, using Autodock-GPU on Summit, it is possible to perform exhaustive docking of one billion compounds in under 24 h. Finally, we discuss preliminary results and planned improvements to the pipeline, including the use of quantum mechanical (QM), machine learning, and artificial intelligence (AI) methods to cluster MD trajectories and rescore docking poses.

60 APPLIED LIFE SCIENCES↗

Large-scale experimental validation of thermochemical water-splitting oxides discovered by defect graph neural networks

Thermochemical water-splitting (TCH) based on 2-step thermal redox cycles in metal oxides is a promising approach to generating H 2 , but state-of-the-art (SOTA) CeO 2 has several practical limitations, which has motivated continued materials discovery efforts in this field. Here, in this study, we improve upon a SOTA defect graph neural network (dGNN) surrogate model's oxygen vacancy predictions and combine them with materials project phase diagrams to down-select and discover structurally diverse, experimentally known metal oxides whose TCH performance was previously unknown. Amongst twelve candidates selected based on our high-throughput screening and down-selection criteria, we achieved ∼80% accuracy in identifying materials with stable redox cycling and hydrogen production in stagnation flow reactor water-splitting experiments. Closer to 100% accuracy can be achieved if higher-accuracy, hybrid DFT-predicted vacancy formation energies were computed and used in lieu of the most uncertain dGNN-based screening predictions, as they correct false positives to true negatives. Notably, two discovered candidates, Sr 3 PrMn 2 O 8 and Ba 2 Fe 2 O 5 , display hydrogen yields greater than CeO 2 under specific redox conditions. In conclusion, these results demonstrate our ability to computationally predict and experimentally validate promising candidate TCH materials that have the potential to compete with CeO 2 .

08 HYDROGEN↗

Cyber Infrastructure for the Smart Electric Grid

As electric power systems undergo a transformative upgrade with the integration of advanced technologies to enable the smarter electric grid, professionals who work in the area require a new understanding of the evolving complexity of the grid. Cyber Infrastructure for the Smart Electric Grid delivers a comprehensive overview of the fundamental principles of smart grid operation and control, smart grid technologies, including sensors, communication networks, computation, data management, and cyber security, and the interdependencies between the component technologies on which a smart grid's security depends. The book offers readers the opportunity to critically analyze the smart grid infrastructure needed to sense, communicate, compute, and control in a secure way.

communication networks↗

Visualisation and outlier detection for probability density function ensembles

Abstract Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks.

97 MATHEMATICS AND COMPUTING↗

Special Issue: Geostatistics and Machine Learning

Abstract Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes.

58 GEOSCIENCES↗

A series representation of the discrete fractional Laplace operator of arbitrary order

Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are greater than one. In this article, we define and study the discrete fractional Laplace operator of arbitrary real-valued positive order. Here a series representation of the discrete fractional Laplace operator for positive non-integer powers is developed. Its convergence to a series representation of a known case of positive integer powers is proven as the power tends to the integer value. Furthermore, we show that the new representation for arbitrary real-valued positive powers of the discrete Laplace operator is consistent with existing theoretical results.

97 MATHEMATICS AND COMPUTING↗

From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas

Functional data analysis (FDA), which is a branch of statistics on modeling infinite dimensional random vectors resided in functional spaces, has become a major research area for Journal of Multivariate Analysis. We review some fundamental concepts of FDA, their origins and connections from multivariate analysis, and some of its recent developments, including multi-level functional data analysis, high-dimensional functional regression, and dependent functional data analysis. Here, we also discuss the impact of these new methodology developments on genetics, plant science, wearable device data analysis, image data analysis, and business analytics. Two real data examples are provided to motivate our discussions.

97 MATHEMATICS AND COMPUTING↗

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Espresso is a beverage brewed using hot, high-pressure water forced through a bed of roasted coffee. Despite being one of the most widely consumed coffee formats, it is also the most susceptible to variation. Here, we report a novel model, complimented by experiment, that is able to isolate the contributions of several brewing variables, thereby disentangling some of the sources of variation in espresso extraction. Under the key assumption of homogeneous flow through the coffee bed, a monotonic decrease in extraction yield with increasingly coarse grind settings is predicted. However, experimental measurements show a peak in the extraction yield versus grind setting relationship, with lower extraction yields at both very coarse and fine settings. This result strongly suggests that inhomogeneous flow is operative at fine grind settings, resulting in poor reproducibility and wasted raw material. With instruction from our model, we outline a procedure to eliminate these shortcomings.

97 MATHEMATICS AND COMPUTING↗

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

97 MATHEMATICS AND COMPUTING↗

A mathematical model of asynchronous data flow in parallel computers *

Abstract We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment’s processing capabilities on the progress of the modelled computation.

Barnard, Richard C.↗