1,220 research outputs found

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics

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    It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM “Schwingungen in rotierenden Maschinen”. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name “European Conference on Rotordynamics”. This new international profile has also been emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations

    A Fast Geometric Multigrid Method for Curved Surfaces

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    We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle meshes to other surface representations like point clouds, nonmanifold meshes, and polygonal meshes. To build the prolongation operators, we associate each point of the hierarchy to a triangle constructed from points in the next coarser level. We obtain well-shaped candidate triangles by computing graph Voronoi diagrams centered around the coarse points and determining neighboring Voronoi cells. Our selection of triangles ensures that the connections of each point to points at adjacent coarser and finer levels are balanced in the tangential directions. As a result, we obtain sparse prolongation matrices with three entries per row and fast convergence of the solver.Comment: Ruben Wiersma and Ahmad Nasikun contributed equally. To be published in SIGGRAPH 2023. 16 pages total (8 main, 5 supplement), 14 figure

    Enabling dynamic and intelligent workflows for HPC, data analytics, and AI convergence

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    The evolution of High-Performance Computing (HPC) platforms enables the design and execution of progressively larger and more complex workflow applications in these systems. The complexity comes not only from the number of elements that compose the workflows but also from the type of computations they perform. While traditional HPC workflows target simulations and modelling of physical phenomena, current needs require in addition data analytics (DA) and artificial intelligence (AI) tasks. However, the development of these workflows is hampered by the lack of proper programming models and environments that support the integration of HPC, DA, and AI, as well as the lack of tools to easily deploy and execute the workflows in HPC systems. To progress in this direction, this paper presents use cases where complex workflows are required and investigates the main issues to be addressed for the HPC/DA/AI convergence. Based on this study, the paper identifies the challenges of a new workflow platform to manage complex workflows. Finally, it proposes a development approach for such a workflow platform addressing these challenges in two directions: first, by defining a software stack that provides the functionalities to manage these complex workflows; and second, by proposing the HPC Workflow as a Service (HPCWaaS) paradigm, which leverages the software stack to facilitate the reusability of complex workflows in federated HPC infrastructures. Proposals presented in this work are subject to study and development as part of the EuroHPC eFlows4HPC project.This work has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955558. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and Spain, Germany, France, Italy, Poland, Switzerland and Norway. In Spain, it has received complementary funding from MCIN/AEI/10.13039/501100011033, Spain and the European Union NextGenerationEU/PRTR (contracts PCI2021-121957, PCI2021-121931, PCI2021-121944, and PCI2021-121927). In Germany, it has received complementary funding from the German Federal Ministry of Education and Research (contracts 16HPC016K, 6GPC016K, 16HPC017 and 16HPC018). In France, it has received financial support from Caisse des dépôts et consignations (CDC) under the action PIA ADEIP (project Calculateurs). In Italy, it has been preliminary approved for complimentary funding by Ministero dello Sviluppo Economico (MiSE) (ref. project prop. 2659). In Norway, it has received complementary funding from the Norwegian Research Council, Norway under project number 323825. In Switzerland, it has been preliminary approved for complimentary funding by the State Secretariat for Education, Research, and Innovation (SERI), Norway. In Poland, it is partially supported by the National Centre for Research and Development under decision DWM/EuroHPCJU/4/2021. The authors also acknowledge financial support by MCIN/AEI /10.13039/501100011033, Spain through the “Severo Ochoa Programme for Centres of Excellence in R&D” under Grant CEX2018-000797-S, the Spanish Government, Spain (contract PID2019-107255 GB) and by Generalitat de Catalunya, Spain (contract 2017-SGR-01414). Anna Queralt is a Serra Húnter Fellow.With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2018-000797-S)

    ACiS: smart switches with application-level acceleration

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    Network performance has contributed fundamentally to the growth of supercomputing over the past decades. In parallel, High Performance Computing (HPC) peak performance has depended, first, on ever faster/denser CPUs, and then, just on increasing density alone. As operating frequency, and now feature size, have levelled off, two new approaches are becoming central to achieving higher net performance: configurability and integration. Configurability enables hardware to map to the application, as well as vice versa. Integration enables system components that have generally been single function-e.g., a network to transport data—to have additional functionality, e.g., also to operate on that data. More generally, integration enables compute-everywhere: not just in CPU and accelerator, but also in network and, more specifically, the communication switches. In this thesis, we propose four novel methods of enhancing HPC performance through Advanced Computing in the Switch (ACiS). More specifically, we propose various flexible and application-aware accelerators that can be embedded into or attached to existing communication switches to improve the performance and scalability of HPC and Machine Learning (ML) applications. We follow a modular design discipline through introducing composable plugins to successively add ACiS capabilities. In the first work, we propose an inline accelerator to communication switches for user-definable collective operations. MPI collective operations can often be performance killers in HPC applications; we seek to solve this bottleneck by offloading them to reconfigurable hardware within the switch itself. We also introduce a novel mechanism that enables the hardware to support MPI communicators of arbitrary shape and that is scalable to very large systems. In the second work, we propose a look-aside accelerator for communication switches that is capable of processing packets at line-rate. Functions requiring loops and states are addressed in this method. The proposed in-switch accelerator is based on a RISC-V compatible Coarse Grained Reconfigurable Arrays (CGRAs). To facilitate usability, we have developed a framework to compile user-provided C/C++ codes to appropriate back-end instructions for configuring the accelerator. In the third work, we extend ACiS to support fused collectives and the combining of collectives with map operations. We observe that there is an opportunity of fusing communication (collectives) with computation. Since the computation can vary for different applications, ACiS support should be programmable in this method. In the fourth work, we propose that switches with ACiS support can control and manage the execution of applications, i.e., that the switch be an active device with decision-making capabilities. Switches have a central view of the network; they can collect telemetry information and monitor application behavior and then use this information for control, decision-making, and coordination of nodes. We evaluate the feasibility of ACiS through extensive RTL-based simulation as well as deployment in an open-access cloud infrastructure. Using this simulation framework, when considering a Graph Convolutional Network (GCN) application as a case study, a speedup of on average 3.4x across five real-world datasets is achieved on 24 nodes compared to a CPU cluster without ACiS capabilities

    Algebraic Temporal Blocking for Sparse Iterative Solvers on Multi-Core CPUs

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    Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety of approaches has been proposed to make these polynomial evaluations explicit (i.e., fix the coefficients), e.g., polynomial preconditioners or s-step Krylov methods. Furthermore, it is nowadays a popular practice to approximate triangular solves by a matrix polynomial to increase parallelism. Such algorithms allow to evaluate the polynomial using a so-called matrix power kernel (MPK), which computes the product between a power of a sparse matrix A and a dense vector x, or a related operation. Recently we have shown that using the level-based formulation of sparse matrix-vector multiplications in the Recursive Algebraic Coloring Engine (RACE) framework we can perform temporal cache blocking of MPK to increase its performance. In this work, we demonstrate the application of this cache-blocking optimization in sparse iterative solvers. By integrating the RACE library into the Trilinos framework, we demonstrate the speedups achieved in preconditioned) s-step GMRES, polynomial preconditioners, and algebraic multigrid (AMG). For MPK-dominated algorithms we achieve speedups of up to 3x on modern multi-core compute nodes. For algorithms with moderate contributions from subspace orthogonalization, the gain reduces significantly, which is often caused by the insufficient quality of the orthogonalization routines. Finally, we showcase the application of RACE-accelerated solvers in a real-world wind turbine simulation (Nalu-Wind) and highlight the new opportunities and perspectives opened up by RACE as a cache-blocking technique for MPK-enabled sparse solvers.Comment: 25 pages, 11 figures, 3 table

    Open Problems in (Hyper)Graph Decomposition

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    Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final application concerns a different problem (such as traversal, finding paths, trees, and flows), decomposing large graphs is often an important subproblem for complexity reduction or parallelization. This report is a summary of discussions that happened at Dagstuhl seminar 23331 on "Recent Trends in Graph Decomposition" and presents currently open problems and future directions in the area of (hyper)graph decomposition

    Lattice Boltzmann Methods for Partial Differential Equations

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    Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions
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