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At least 253 records · Page 14

Scaling up to address data science challenges

Statistics and Data Science provide a variety of perspectives and technical approaches for exploring and understanding Big Data. Partnerships between scientists from different fields such as statistics, machine learning, computer science, and applied mathematics can lead to innovative approaches for addressing problems involving increasingly large amounts of data in a rigorous and effective manner that takes advantage of advances in computing. Here, this article will explore various challenges in Data Science and will highlight statistical approaches that can facilitate analysis of large-scale data including sampling and data reduction methods, techniques for effective analysis and visualization of large-scale simulations, and algorithms and procedures for efficient processing.

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↗

Validation Metrics for Deterministic and Probabilistic Data

Computational modeling and simulation are paramount to modern science. Computational models often replace physical experiments that are prohibitively expensive, dangerous, or occur at extreme scales. Thus, it is critical that these models accurately represent and can be used as replacements for reality. This paper provides an analysis of metrics that may be used to determine the validity of a computational model. While some metrics have a direct physical meaning and a long history of use, others, especially those that compare probabilistic data, are more difficult to interpret. Furthermore, the process of model validation is often application-specific, making the procedure itself challenging and the results difficult to defend. We therefore provide guidance and recommendations as to which validation metric to use, as well as how to use and decipher the results. Furthermore an example is included that compares interpretations of various metrics and demonstrates the impact of model and experimental uncertainty on validation processes.

97 MATHEMATICS AND COMPUTING↗

Teaching Computational Reproducibility for Neuroimaging

We describe a project-based introduction to reproducible and collaborative neuroimaging analysis. Traditional teaching on neuroimaging usually consists of a series of lectures that emphasize the big picture rather than the foundations on which the techniques are based. The lectures are often paired with practical workshops in which students run imaging analyses using the graphical interface of specific neuroimaging software packages. Our experience suggests that this combination leaves the student with a superficial understanding of the underlying ideas, and an informal, inefficient, and inaccurate approach to analysis. To address these problems, we based our course around a substantial open-ended group project. This allowed us to teach: (a) computational tools to ensure computationally reproducible work, such as the Unix command line, structured code, version control, automated testing, and code review and (b) a clear understanding of the statistical techniques used for a basic analysis of a single run in an MR scanner. The emphasis we put on the group project showed the importance of standard computational tools for accuracy, efficiency, and collaboration. The projects were broadly successful in engaging students in working reproducibly on real scientific questions. We propose that a course on this model should be the foundation for future programs in neuroimaging. We believe it will also serve as a model for teaching efficient and reproducible research in other fields of computational science.

60 APPLIED LIFE SCIENCES↗

Women in Science: Fermilab Scientific Computing Specialist Krista Majewski

With February 11 marking the International Day of Women and Girls in Science, female physicists, engineers and computer scientists from CERN and Fermilab share their experiences of building careers in science. Krista Majewski came to Fermilab nine years ago as a software developer and now works in an operations role. She is a computing services specialist and part of the grid and cloud operations group, which manages computing clusters for the CMS experiment and other intensity frontier experiments at the lab. "My typical day would be maintaining the services that our group is responsible for and the machines that they run on. So if there are problems with a computing cluster where a user can't run their jobs, or they're trying to run on resources on the grid and they're unable to, then our group would be responsible for helping debug some of those issues," Krista says. Her path to programming at Fermilab has been winding. After receiving a degree in biomedical engineering, she went to work doing web development and programming for a large consulting firm, then moved to the financial industry. But programming called her back, and she earned a master's degree in computer science to start her new career. For Krista, programming is similar to something she enjoyed as child: solving puzzles. "I think it's a skill that you use in a lot of different ways," she says. Credits: Video production - Fermilab Creative Services Music Copyright: Universal Production Music Astral Light Chevalier Idea originally conceived by Tanya Levshina, Fermilab and Maria Dimou, CERN.

99 GENERAL AND MISCELLANEOUS↗

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↗

The future of computing beyond Moore’s Law

Moore’s Law is a techno-economic model that has enabled the information technology industry to double the performance and functionality of digital electronics roughly every 2 years within a fixed cost, power and area. Advances in silicon lithography have enabled this exponential miniaturization of electronics, but, as transistors reach atomic scale and fabrication costs continue to rise, the classical technological driver that has underpinned Moore’s Law for 50 years is failing and is anticipated to flatten by 2025. Here, this article provides an updated view of what a post-exascale system will look like and the challenges ahead, based on our most recent understanding of technology roadmaps. It also discusses the tapering of historical improvements, and how it affects options available to continue scaling of successors to the first exascale machine. Lastly, this article covers the many different opportunities and strategies available to continue computing performance improvements in the absence of historical technology drivers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

97 MATHEMATICS AND COMPUTING↗

Visualization and Simulation of Carbon Structures with Higher Genus

The Computational Science Initiative (CSI) department at Brookhaven National Laboratory involves varied and interdisciplinary work through out all sciences. In particular, we worked within the realm of computational chemistry through the means of studying carbon nanotori structures via their visualization and simulation. Compounds like graphene and other carbon allotropes,such as the nanotorus, have been in the eye of scientists for several years due to their unique polyhex structures which provide unique topologies and therefore possibly unique material properties. C++ code to generate Cartesian coordinates for an arbitrary torus was utilized to allow the use of molecular editing and modeling programs, such as Avogadro or Visual Molecular Dynamics (VMD) to design multiple genus nanocarbon toroidal structures. Several files were generated that contained multiple genus to them, namely a double torus, triple torus, and quadruple torus, all based off of a single genus carbon nanotorus from previous said code. Bond angle information was then utilized through .report files generated from structures files (.xyz or .cml) to allow for vertices and thereby neighboring atoms to the vertices to be identified. With these identified atoms for the above multiple genus structures, as well as for the C240 buckyball fullerene and carbon nanotorus, we wrote C++ code to generate an adjacency matrix for each respective one. These matrices were then subsequently used to generate eigenvalues and eigenvectors through a Mathmatica function for each structure. Using these values we can study the energies of these systems and thereby its functionalities and properties.

97 MATHEMATICS AND COMPUTING↗

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↗

VERAIn

CASL's modeling and simulation technology, the Virtual Environment for Reactor Applications (VERA), incorporates coupled physics and science-based models, state-of-the-art numerical methods, modern computational science, integrated uncertainty quantification (UQ) and validation against data from operating pressurized water reactors (PWRs), single-effect experiments, and integral tests. The computational simulation component of VERA is the VERA Core Simulator (VERA-CS). The core simulator is the specific collection of multi-physics computer codes used to model and deplete a LWR core over multiple cycles. The core simulator has a single common input file that drives all of the different physics codes. The parser code, VERAIn, converts VERA Input into an XML file that is used as input to different VERA codes.

Simunovic, Srdjan↗

VERAIn

CASL's modeling and simulation technology, the Virtual Environment for Reactor Applications (VERA), incorporates coupled physics and science-based models, state-of-the-art numerical methods, modern computational science, integrated uncertainty quantification (UQ) and validation against data from operating pressurized water reactors (PWRs), single-effect experiments, and integral tests. The computational simulation component of VERA is the VERA Core Simulator (VERA-CS). The core simulator is the specific collection of multi-physics computer codes used to model and deplete a LWR core over multiple cycles. The core simulator has a single common input file that drives all of the different physics codes. The parser code, VERAIn, converts VERA Input into an XML file that is used as input to different VERA codes.

Simunovic, Srdjan↗

Dehydration pathways of 1-propanol on HZSM-5 in the presence and absence of water

The Brønsted acid-catalyzed gas-phase dehydration of 1-propanol (0.075-4 kPa) was studied on zeolite H-MFI (Si/Al = 26, containing minimal amounts of extraframework Al moieties) in the absence and presence of co-fed water (0-2.5 kPa) at 413-443 K. It is shown that propene can be formed from monomeric and dimeric adsorbed 1-propanol. The stronger adsorption of 1-propanol relative to water indicates that the reduced dehydration rates in the presence of water are not a consequence of the competitive adsorption between 1-propanol and water. Instead, the deleterious effect is related to the different extents of stabilization of adsorbed intermediates and the relevant elimination/substitution transition states by water. Water stabilizes the adsorbed 1-propanol monomer significantly more than the elimination transition state, leading to a higher activation barrier and a greater entropy gain for the rate-limiting step, which eventually leads to propene. In a similar manner, an excess of 1-propanol stabilizes the adsorbed state of 1-propanol more than the elimination transition state. In comparison with the monomer-mediated pathway, adsorbed dimer and the relevant transition states for propene and ether formation are similarly, while less effectively, stabilized by intrazeolite water molecules. This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, and was performed in part using the Molecular Sciences Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory, a DOE national scientific user facility sponsored by the DOE’s Office of Biological and Environmental Research and located and the Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for DOE.

1-propanol↗