ASCR/HEP Exascale Requirements Review Report

This draft report summarizes and details the findings, results, and recommendations derived from the ASCR/HEP Exascale Requirements Review meeting held in June, 2015. The main conclusions are as follows. 1) Larger, more capable computing and data facilities are needed to support HEP science goals in all three frontiers: Energy, Intensity, and Cosmic. The expected scale of the demand at the 2025 timescale is at least two orders of magnitude -- and in some cases greater -- than that available currently. 2) The growth rate of data produced by simulations is overwhelming the current ability, of both facilities and researchers, to store and analyze it. Additional resources and new techniques for data analysis are urgently needed. 3) Data rates and volumes from HEP experimental facilities are also straining the ability to store and analyze large and complex data volumes. Appropriately configured leadership-class facilities can play a transformational role in enabling scientific discovery from these datasets. 4) A close integration of HPC simulation and data analysis will aid greatly in interpreting results from HEP experiments. Such an integration will minimize data movement and facilitate interdependent workflows. 5) Long-range planning between HEP and ASCR will be required to meet HEP's research needs. To best use ASCR HPC resources the experimental HEP program needs a) an established long-term plan for access to ASCR computational and data resources, b) an ability to map workflows onto HPC resources, c) the ability for ASCR facilities to accommodate workflows run by collaborations that can have thousands of individual members, d) to transition codes to the next-generation HPC platforms that will be available at ASCR facilities, e) to build up and train a workforce capable of developing and using simulations and analysis to support HEP scientific research on next-generation systems.Comment: 77 pages, 13 Figures; draft report, subject to further revisio

Multi-Architecture Monte-Carlo (MC) Simulation of Soft Coarse-Grained Polymeric Materials: SOft coarse grained Monte-carlo Acceleration (SOMA)

Multi-component polymer systems are important for the development of new materials because of their ability to phase-separate or self-assemble into nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction with a soft, coarse-grained polymer model is an established technique to investigate these soft-matter systems. Here we present an im- plementation of this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is suitable to simulate large system sizes with up to billions of particles, yet versatile enough to study properties of different kinds of molecular architectures and interactions. We achieve efficiency of the simulations commissioning accelerators like GPUs on both workstations as well as supercomputers. The implementa- tion remains flexible and maintainable because of the implementation of the scientific programming language enhanced by OpenACC pragmas for the accelerators. We present implementation details and features of the program package, investigate the scalability of our implementation SOMA, and discuss two applications, which cover system sizes that are difficult to reach with other, common particle-based simulation methods

Optimization of a parallel Monte Carlo method for linear algebra problems

Many problems in science and engineering can be represented by Systems of Linear Algebraic Equations (SLAEs). Numerical methods such as direct or iterative ones are used to solve these kind of systems. Depending on the size and other factors that characterize these systems they can be sometimes very difficult to solve even for iterative methods, requiring long time and large amounts of computational resources. In these cases a preconditioning approach should be applied. Preconditioning is a technique used to transform a SLAE into a equivalent but simpler system which requires less time and effort to be solved. The matrix which performs such transformation is called the preconditioner [7]. There are preconditioners for both direct and iterative methods but they are more commonly used among the later ones. In the general case a preconditioned system will require less effort to be solved than the original one. For example, when an iterative method is being used, less iterations will be required or each iteration will require less time, depending on the quality and the efficiency of the preconditioner. There are different classes of preconditioners but we will focused only on those that are based on the SParse Approximate Inverse (SPAI) approach. These algorithms are based on the fact that the approximate inverse of a given SLAE matrix can be used to approximate its result or to reduce its complexity. Monte Carlo methods are probabilistic methods, that use random numbers to either simulate a stochastic behaviour or to estimate the solution of a problem. They are good candidates for parallelization due to the fact that many independent samples are used to estimate the solution. These samples can be calculated in parallel, thereby speeding up the solution finding process [27]. In the past there has been a lot of research around the use of Monte Carlo methods to calculate SPAI preconditioners [1] [27] [10]. In this work we present the implementation of a SPAI preconditioner that is based on a Monte Carlo method. This algorithm calculates the matrix inverse by sampling a random variable which approximates the Neumann Series expansion. Using the Neumman series it is possible to calculate the matrix inverse of a system A by performing consecutive additions of the powers of a matrix expressed by the series expansion of (I − A) −1 . Given the stochastic approach of the Monte Carlo algorithm, the computational effort required to find an element of the inverse matrix is independent from the size of the matrix. This allows to target systems that, due to their size, can be prohibitive for common deterministic approaches [27]. Great part of this work is focused on the enhancement of this algorithm. First, the current errors of the implementation were fixed, making the algorithm able to target larger systems. Then multiple optimizations were applied at different stages of the implementation making a better use of the resources and improving the performance of the algorithm. Four optimizations, with consistently improvements have been performed: 1. An inefficient implementation of the realloc function within the MPI library was provoking the application to rapidly run out of memory. This function was replaced by the malloc function and some slight modifications to estimate the size of matrix A. 2. A coordinate format (COO) was introduced within the algorithm’s core to make a more efficient use of the memory, avoiding several unnecessary memory accesses. 3. A method to produce an intermediate matrix P was shown to produce similar results to the default one and with matrix P being reduced to a single vector, thus requiring less data. Given that this was a broadcast data a diminishing on it, translated into a reduction of the broadcast time. 4. Four individual procedures which accessed the whole initial matrix memory, were merged into two processes, reducing this way the number of memory accesses. For each optimization applied, a comparison was performed to show the particular improvements achieved. A set of different matrices, representing different SLAEs, was used to show the consistency of these improvements. In order to provide with insights about the scalability issues of the algorithm, other approaches are presented to show the particularities of the algorithm’s scalability: 1. Given that the original version of this algorithm was designed for a cluster of single-core machines, an hybrid approach of MPI + openMP was proposed to target the nowadays multi-core architectures. Surprisingly this new approach did not show any improvement but it was useful to show a scalability problem related to the random pattern used to access the memory. 2. Having that common MPI implementations of the broadcast operation do not take into account the different latencies between inter-node and intra-node communications [25]. Therefore, we decided to implement the broadcast in two steps. First by reaching a single process in each of the compute nodes and then using those processes to perform a local broadcast within their compute nodes. Results on this approach showed that this method could lead to improvements when very big systems are used. Finally a comparison is carried out between the optimized version of the Monte Carlo algorithm and the state of the art Modified SPAI (MSPAI). Four metrics are used to compare these approaches: 1. The amount of time needed for the preconditioner construction. 2. The time needed by the solver to calculate the solution of the preconditioned system. 3. The addition of the previous metrics, which gives a overview of the quality and efficiency of the preconditioner. 4. The number of cores used in the preconditioner construction. This gives an idea of the energy efficiency of the algorithm. Results from previous comparison showed that Monte Carlo algorithm can deal with both symmetric and nonsymmetric matrices while MSPAI only performs well with the nonsymetric ones. Furthermore the time for Monte Carlo’s algorithm is always faster for the preconditioner construction and most of the times also for the solver calculation. This means that Monte Carlo produces preconditioners of better or same quality than MSPAI. Finally, the number of cores used in the Monte Carlo approach is always equal or smaller than in the case of MSPAI

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Towards a Mini-App for Smoothed Particle Hydrodynamics at Exascale

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics represent computationally-demanding calculations. The parallelization of SPH codes is not trivial due to the absence of a structured grid. Additionally, the performance of the SPH codes can be, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. This work presents insights into the current performance and functionalities of three SPH codes: SPHYNX, ChaNGa, and SPH-flow. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH mini-app. To gain such insights, a rotating square patch test was implemented as a common test simulation for the three SPH codes and analyzed on two modern HPC systems. Furthermore, to stress the differences with the codes stemming from the astrophysics community (SPHYNX and ChaNGa), an additional test case, the Evrard collapse, has also been carried out. This work extrapolates the common basic SPH features in the three codes for the purpose of consolidating them into a pure-SPH, Exascale-ready, optimized, mini-app. Moreover, the outcome of this serves as direct feedback to the parent codes, to improve their performance and overall scalability.Comment: 18 pages, 4 figures, 5 tables, 2018 IEEE International Conference on Cluster Computing proceedings for WRAp1

SPH-EXA: Enhancing the Scalability of SPH codes Via an Exascale-Ready SPH Mini-App

Numerical simulations of fluids in astrophysics and computational fluid dynamics (CFD) are among the most computationally-demanding calculations, in terms of sustained floating-point operations per second, or FLOP/s. It is expected that these numerical simulations will significantly benefit from the future Exascale computing infrastructures, that will perform 10^18 FLOP/s. The performance of the SPH codes is, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. In this work an extensive study of three SPH implementations SPHYNX, ChaNGa, and XXX is performed, to gain insights and to expose any limitations and characteristics of the codes. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH mini-app. We implemented a rotating square patch as a joint test simulation for the three SPH codes and analyzed their performance on a modern HPC system, Piz Daint. The performance profiling and scalability analysis conducted on the three parent codes allowed to expose their performance issues, such as load imbalance, both in MPI and OpenMP. Two-level load balancing has been successfully applied to SPHYNX to overcome its load imbalance. The performance analysis shapes and drives the design of the SPH-EXA mini-app towards the use of efficient parallelization methods, fault-tolerance mechanisms, and load balancing approaches.Comment: arXiv admin note: substantial text overlap with arXiv:1809.0801

Computational Methods in Science and Engineering : Proceedings of the Workshop SimLabs@KIT, November 29 - 30, 2010, Karlsruhe, Germany

In this proceedings volume we provide a compilation of article contributions equally covering applications from different research fields and ranging from capacity up to capability computing. Besides classical computing aspects such as parallelization, the focus of these proceedings is on multi-scale approaches and methods for tackling algorithm and data complexity. Also practical aspects regarding the usage of the HPC infrastructure and available tools and software at the SCC are presented

Parallel cross interpolation for high-precision calculation of high-dimensional integrals

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte Carlo, the samples calculated by our algorithm are neither random nor form a regular lattice. Instead we calculate the given function along individual dimensions (modes) and use these values to reconstruct its behaviour in the whole domain. The positions of the calculated univariate fibres are chosen adaptively for the given function. The required evaluations can be executed in parallel along each mode (variable) and over all modes. To demonstrate the efficiency of the proposed method, we apply it to compute high-dimensional Ising susceptibility integrals, arising from asymptotic expansions for the spontaneous magnetisation in two-dimensional Ising model of ferromagnetism. We observe strong superlinear convergence of the proposed method, while the MC and qMC algorithms converge sublinearly. Using multiple precision arithmetic, we also observe exponential convergence of the proposed algorithm. Combining high-order convergence, almost perfect scalability up to hundreds of processes, and the same flexibility as MC and qMC, the proposed algorithm can be a new method of choice for problems involving high-dimensional integration, e.g. in statistics, probability, and quantum physics