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At least 163 records · Page 9

Optimizing the hypre solver for manycore and GPU architectures

The solution of large-scale combustion problems with codes such as Uintah on modern computer architectures requires the use of multithreading and GPUs to achieve performance. Uintah uses a low-Mach number approximation that requires iteratively solving a large system of linear equations. The Hypre iterative solver has solved such systems in a scalable way for Uintah, but the use of OpenMP with Hypre leads to at least slowdown due to OpenMP overheads. The proposed solution uses the MPI Endpoints within Hypre, where each team of threads acts as a different MPI rank. This approach minimizes OpenMP synchronization overhead and performs as fast or (up to 1.44) faster than Hypre's MPI-only version, and allows the rest of Uintah to be optimized using OpenMP. The profiling of the GPU version of Hypre shows the bottleneck to be the launch overhead of thousands of micro-kernels. The GPU performance was improved by fusing these micro-kernels and was further optimized by using Cuda-aware MPI, resulting in an overall speedup of 1.16—1.44 compared to the baseline GPU implementation. The above optimization strategies were published in the International Conference on Computational Science 2020 [1]. This work extends the previously published research by carrying out the second phase of communication-centered optimizations in Hypre to improve its scalability on large-scale supercomputers. Additionally, this includes an efficient non-blocking inter-thread communication scheme, communication-reducing patch assignment, and expression of logical communication parallelism to a new version of the MPICH library that utilizes the underlying network parallelism [2]. The above optimizations avoid communication bottlenecks previously observed during strong scaling and improve performance by up to 2 on 256 nodes of Intel Knight's Landing processor.

97 MATHEMATICS AND COMPUTING↗

Towards large-scale quantum optimization solvers with few qubits

Quantum computers hold the promise of more efficient combinatorial optimization solvers, which could be game-changing for a broad range of applications. However, a bottleneck for materializing such advantages is that, in order to challenge classical algorithms in practice, mainstream approaches require a number of qubits prohibitively large for near-term hardware. Here we introduce a variational solver for MaxCut problems over $m={{\mathcal{O}}}({n}^{k})$ binary variables using only n qubits, with tunable k > 1. The number of parameters and circuit depth display mild linear and sublinear scalings in m , respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. Altogether, this leads to high quantum-solver performances. For instance, for m = 7000, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for m = 2000, experiments with n = 17 trapped-ion qubits feature MaxCut approximation ratios estimated to be beyond the hardness threshold 0.941. Our findings offer an interesting heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

97 MATHEMATICS AND COMPUTING↗

Encoding integers and rationals on neuromorphic computers using virtual neuron

Abstract Neuromorphic computers emulate the human brain while being extremely power efficient for computing tasks. In fact, they are poised to be critical for energy-efficient computing in the future. Neuromorphic computers are primarily used in spiking neural network–based machine learning applications. However, they are known to be Turing-complete, and in theory can perform all general-purpose computation. One of the biggest bottlenecks in realizing general-purpose computations on neuromorphic computers today is the inability to efficiently encode data on the neuromorphic computers. To fully realize the potential of neuromorphic computers for energy-efficient general-purpose computing, efficient mechanisms must be devised for encoding numbers. Current encoding mechanisms (e.g., binning, rate-based encoding, and time-based encoding) have limited applicability and are not suited for general-purpose computation. In this paper, we present the virtual neuron abstraction as a mechanism for encoding and adding integers and rational numbers by using spiking neural network primitives. We evaluate the performance of the virtual neuron on physical and simulated neuromorphic hardware. We estimate that the virtual neuron could perform an addition operation using just 23 nJ of energy on average with a mixed-signal, memristor-based neuromorphic processor. We also demonstrate the utility of the virtual neuron by using it in some of the μ -recursive functions, which are the building blocks of general-purpose computation.

97 MATHEMATICS AND COMPUTING↗

A Visual Comparison of Silent Error Propagation

High-performance computing (HPC) systems play a critical role in facilitating scientific discoveries. Their scale and complexity (e.g., the number of computational units and software stack) continue to grow as new systems are expected to process increasingly more data and reduce computing time. However, with more processing elements, the probability that these systems will experience a random bit-flip error that corrupts a program's output also increases, which is often recognized as silent data corruption. Analyzing the resiliency of HPC applications in extreme-scale computing to silent data corruption is crucial but difficult. An HPC application often contains a large number of computation units that need to be tested, and error propagation caused by error corruption is complex and difficult to interpret. Here, to accommodate this challenge, we propose an interactive visualization system that helps HPC researchers understand the resiliency of HPC applications and compare their error propagation. Our system models an application's error propagation to study a program's resiliency by constructing and visualizing its fault tolerance boundary. Coordinating with multiple interactive designs, our system enables domain experts to efficiently explore the complicated spatial and temporal correlation between error propagations. At the end, the system integrated a nonmonotonic error propagation analysis with an adjustable graph propagation visualization to help domain experts examine the details of error propagation and answer such questions as why an error is mitigated or amplified by program execution.

97 MATHEMATICS AND COMPUTING↗

EdgeAI: How to Use AI to Collect Reliable and Relevant Watershed Data

Focal Area(s): Focal areas are on data acquisition and assimilation enabled by AI, advanced methods including experimental/network design/optimization, unsupervised learning (including deep learning), and hardware-related efforts involving AI (e.g., edge computing). Science Challenge: The transformational science challenge that we address is the following: – Ensuring, in near real-time, that the data collected from distributed sensor networks is accurate and contains useful information to identify, quantify, and predict watershed and ecosystem dynamic responses to short- and long-term perturbations.

54 ENVIRONMENTAL SCIENCES↗

Development of an Enhanced Radiation Physics Toolset for Modeling Spectral and Imaging Signatures in the Warm Dense Matter Experiments

Radiative and atomic processes in plasmas play a critical role in a wide variety of high energy density laboratory plasma (HEDLP) experiments. The emission, absorption, and transport of radiation can strongly affect the overall energetics and evolution of such plasmas. In addition, radiation-based diagnostics – including imaging, spectroscopy, and absolute flux measurements – are widely used to determine key features of HEDLPs. To advance our understanding of HEDLP science, it is vital to have high-fidelity computational physics tools that have well-tested radiation physics modeling, and that are readily accessible to researchers in the HEDLP community. Simulations play an extremely important role for planning and designing the experiments, as well as for post-experiment data analysis. Prism Computational Sciences develops software that is used by National Laboratories and universities (including five members of LaserNetUS network). Prominent examples of such research efforts include z-pinch and short-pulse laser experiments designed to study the basic physics of photoionized plasmas and photoionization fronts, as well as their application to astrophysical plasmas. The main effort was dedicated to the development of non-equilibrium equation-of-state (EOS) models within the HELIOS-CR code, a hydrodynamics code with inline collisional-radiative atomic kinetics. Gas cell experiments on Z and Omega demonstrated the importance of non-equilibrium effects on atomic kinetics in photoionized plasmas. Recent proof-of-principle experiments on Omega EP confirmed the advantages of using a short-pulse laser to create an intense radiation drive, leading to additional experiments being proposed. Photoionization front experiments at LLE also emphasizes the importance of radiation and atomic physics. In both studies, HELIOS-CR simulations played a crucial role in computing non-equilibrium opacities and ionization distributions. A newly developed non-LTE EOS model will help addressing possible non-equilibrium effects, on for example specific heat, and their influence in plasma evolution. Prism also implemented support for open-source atomic data generated by the Flexible Atomic Code. This allows researchers to generate custom atomic tables and use them within the complex framework of simulation tools developed by Prism. The ability to use open-source atomic data would be extremely valuable for hydrodynamics and spectroscopic simulations that include high-Z materials, e.g., picosecond x-ray pulse generation experiments. Support for new atomic structures was fully implemented, and the data can be used by all simulation tools developed at Prism: radiation-hydrodynamics, imaging and spectroscopy, EOS and opacity. The development resulted in a significant fidelity enhancement to the simulations tools developed by Prism that are currently used in other cutting-edge experiments including: opacity measurement experiments performed to both understand the basic radiative and atomic properties of plasmas as well as provide data for more accurately modeling the internal structure of the Sun and other stars, high-intensity short-pulse laser experiments performed to develop short-wavelength light sources for use as backlighters and to investigate fast ignition concepts for inertial fusion energy; capsule implosion experiments designed to develop inertial fusion as an energy source, etc.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Classical optimization with imaginary-time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. Here, we develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Zhong, Dawei [University of Southern California, L↗

Smoky Mountain Data Challenge 2020: An Open Call to Solve Data Problems in the Areas of Neutron Science, Material Science, Urban Modeling and Dynamics, Geophysics, and Biomedical Informatics

The 2020 Smoky Mountains Computational Sciences and Engineering Conference enlists research scientists from across Oak Ridge National Laboratory (ORNL) to be data sponsors and help create data analytics challenges for eminent data sets at the laboratory. This work describes the significance of each of the seven data sets and their as- sociated challenge questions. The challenge questions for each data set were required to cover multiple difficulty levels. An international call for participation was sent to students, and researchers asking them to form teams of up to four people to apply novel data analytics techniques to these data sets.

Parete-Koon, Suzanne↗

Circuit complexity and functionality: A statistical thermodynamics perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

Science & Technology - Other Topics↗

Engineering Computational Practices (Rev. 1)

This manual will attempt to motivate the use of an automated build system for the purposes of computational science and engineering. As part of this motivation, the surrounding computational practices of version control, documen tation, compute environment management, and regression testing will also be addressed as applied to the practice of computational engineering. Specifically, this manual intends to motivate the adoption of these traditional software engineering practices for use in research and production engineering simulation projects. This manual is not the first such effort in the greater scientific computing community. In fact, the authors relied heavily on the lesson plans of the Software Carpentry, established to teach computing skills to researchers in 1998. As the intention for this manual is to lay out fundamental practices of engineering computing, it will not attempt to fully teach the underlying concepts and will instead reference the well designed lesson plans of the Software Carpentry. Where possible, this manual will explain to general computing practices and concepts and limit discussion of specific software implementations to examples or vehicles for practice in concrete application. The specific software taught by the Software Carpentry curriculum is an excellent starting point to learn the core concepts of computational engi neering. However, the authors have found that applications to engineering simulation and analysis require translation of these software development concepts into the language and workflows of computational engineers. Adopting these computational tools may require engineers to re-imagine their workflows in some combination of traditional engineer ing and software concepts. It has also been necessary to extend existing software build systems for engineering practices beyond the simple wrap ping of engineering software execution. Where necessary, examples of specific software and their method of extension to engineering simulations will be given, with reference to the User Manual for recommended practical use. Where this manual relies on specific implementation examples, it should be understood that the practicing engineer may find that different software is more amenable to their specific work. It is always the overall collection of computational practices is more important than any specific software implementation. The ability to recognize which concepts are implemented by a software package will make a practicing engineer agile to changing project needs, computing resources, numeric solvers, programming languages, and even available funding.

42 ENGINEERING↗

Teaching Quantum Computing to High School Students

Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years old. This course was designed to bridge the gap between popular science articles and advanced undergraduate textbooks. Conceptual ideas in the text are reinforced with active learning techniques, such as interactive problem sets and simulation-based labs at various levels. The course is freely available for use and download under the Creative Commons “Attribution-NonCommercial-ShareAlike 4.0 International” license.

97 MATHEMATICS AND COMPUTING↗

Differentiating densities on smooth manifolds

Lebesgue integration of derivatives of strongly-oscillatory functions is a recurring challenge in computational science and engineering. Integration by parts is an effective remedy for huge computational costs associated with Monte Carlo integration schemes. In case of Lebesgue integrals over a smooth manifold, however, integration by parts gives rise to a derivative of the density implied by charts describing the domain manifold. This paper focuses on the computation of that derivative, which we call the density gradient function, on general smooth manifolds. We analytically derive formulas for the density gradient and present examples of manifolds determined by popular differential equation-driven systems. Furthermore, we highlight the significance of the density gradient by demonstrating a numerical example of Monte Carlo integration involving oscillatory integrands.

97 MATHEMATICS AND COMPUTING↗

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization. In this work, we introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

97 MATHEMATICS AND COMPUTING↗

Elucidating and predicting the dynamic evolution of water and land systems due to natural and energy-related forcings

Focal Area(s): 3. Insight gleaned from complex data (both observed and simulated) using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI; & 1. Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, unsupervised learning (including deep learning), and hardware-related efforts involving AI (e.g., edge computing). Science Challenge: Interactions between water, land, and energy systems are complex and occur on a variety of scales, ranging from local to basinal to regional. Accurately predicting the behavior of ground water and surface water systems for 5-10 years and beyond requires an understanding of the current system and the ability to model both the natural system at scale and human-induced forcings related to energy and other activities. Artificial intelligence and machine learning (AI/ML) combined with modern compilation and integration efforts for U.S. groundwater and surface water systems present potential solutions to bolstering detailed physics-based models of these systems. Big data tied with ML and physics-based modeling can drive breakthroughs in understanding the earth system, but research is often impeded by data access (e.g., privacy issues), quality, formats, gaps, multi-source, multi-scale, integration, and spatiotemporal challenges. Effective integration of real data and simulated (synthetic) data that fill gaps is critical. Overcoming these complex data and model integration challenges will enable a transformational approach to acquiring enhanced understanding of environmental systems.

54 ENVIRONMENTAL SCIENCES↗

A Brief Overview of Radiochemistry: Californium-252: Unique and Versatile Man-made Radioisotope

This chapter summarizes radiochemistry and its applications with a focus on areas where computational science can be beneficial. This is presented for a target audience of computational scientists and chemists, and the general public who are interested in radiochemistry topics that may benefit from the use of computational methods. Past, present, and future applications of radiochemistry are presented along with a brief examination of the field’s workforce. Discussions of the current state of several radiochemistry specialty areas are also included. These discussions generally exemplify topics that are readily amenable to computational tools. Topics discussed include medical uses for radioactive materials and related computational needs; the current and future trends in the separations of the f-block elements; production and uses of Californium-252; and the need for exascale computing to solve current problems in the chemistry of Americium and Plutonium.

Ezold, Julie↗