Batched Linear Algebra Problems on GPU Accelerators

The emergence of multicore and heterogeneous architectures requires many linear algebra algorithms to be redesigned to take advantage of the accelerators, such as GPUs. A particularly challenging class of problems, arising in numerous applications, involves the use of linear algebra operations on many small-sized matrices. The size of these matrices is usually the same, up to a few hundred. The number of them can be thousands, even millions. Compared to large matrix problems with more data parallel computation that are well suited on GPUs, the challenges of small matrix problems lie in the low computing intensity, the large sequential operation fractions, and the big PCI-E overhead. These challenges entail redesigning the algorithms instead of merely porting the current LAPACK algorithms. We consider two classes of problems. The first is linear systems with one-sided factorizations (LU, QR, and Cholesky) and their solver, forward and backward substitution. The second is a two-sided Householder bi-diagonalization. They are challenging to develop and are highly demanded in applications. Our main efforts focus on the same-sized problems. Variable-sized problems are also considered, though to a lesser extent. Our contributions can be summarized as follows. First, we formulated a batched linear algebra framework to solve many data-parallel, small-sized problems/tasks. Second, we redesigned a set of fundamental linear algebra algorithms for high- performance, batched execution on GPU accelerators. Third, we designed batched BLAS (Basic Linear Algebra Subprograms) and proposed innovative optimization techniques for high-performance computation. Fourth, we illustrated the batched methodology on real-world applications as in the case of scaling a CFD application up to 4096 nodes on the Titan supercomputer at Oak Ridge National Laboratory (ORNL). Finally, we demonstrated the power, energy and time efficiency of using accelerators as compared to CPUs. Our solutions achieved large speedups and high energy efficiency compared to related routines in CUBLAS on NVIDIA GPUs and MKL on Intel Sandy-Bridge multicore CPUs. The modern accelerators are all Single-Instruction Multiple-Thread (SIMT) architectures. Our solutions and methods are based on NVIDIA GPUs and can be extended to other accelerators, such as the Intel Xeon Phi and AMD GPUs based on OpenCL

Task-based Runtime Optimizations Towards High Performance Computing Applications

The last decades have witnessed a rapid improvement of computational capabilities in high-performance computing (HPC) platforms thanks to hardware technology scaling. HPC architectures benefit from mainstream advances on the hardware with many-core systems, deep hierarchical memory subsystem, non-uniform memory access, and an ever-increasing gap between computational power and memory bandwidth. This has necessitated continuous adaptations across the software stack to maintain high hardware utilization. In this HPC landscape of potentially million-way parallelism, task-based programming models associated with dynamic runtime systems are becoming more popular, which fosters developers’ productivity at extreme scale by abstracting the underlying hardware complexity. In this context, this dissertation highlights how a software bundle powered by a task-based programming model can address the heterogeneous workloads engendered by HPC applications., i.e., data redistribution, geospatial modeling and 3D unstructured mesh deformation here. Data redistribution aims to reshuffle data to optimize some objective for an algorithm, whose objective can be multi-dimensional, such as improving computational load balance or decreasing communication volume or cost, with the ultimate goal of increasing the efficiency and therefore reducing the time-to-solution for the algorithm. Geostatistical modeling, one of the prime motivating applications for exascale computing, is a technique for predicting desired quantities from geographically distributed data, based on statistical models and optimization of parameters. Meshing the deformable contour of moving 3D bodies is an expensive operation that can cause huge computational challenges in fluid-structure interaction (FSI) applications. Therefore, in this dissertation, Redistribute-PaRSEC, ExaGeoStat-PaRSEC and HiCMA-PaRSEC are proposed to efficiently tackle these HPC applications respectively at extreme scale, and they are evaluated on multiple HPC clusters, including AMD-based, Intel-based, Arm-based CPU systems and IBM-based multi-GPU system. This multidisciplinary work emphasizes the need for runtime systems to go beyond their primary responsibility of task scheduling on massively parallel hardware system for servicing the next-generation scientific applications

Relajaciones de ejecución definidas por el usuario para la mejora de la programabilidad en computación paralela de altas prestaciones

Tesis de la Universidad Complutense de Madrid, Facultad de Informática, leída el 22-11-2019This thesis proposes the development and implementation of a new programming model basedon execution relaxations, and focused on High-Performance Parallel Computing. Specifically,the main goals of the thesis are:1. Advocate a development methodology in which users define the basic computing units(tasks), together with a set of relaxations in, possibly, multiple dimensions. These relaxationswill be translated, at execution time, into expanded (and complex) scheduling opportunitiesdepending on the underlying architectural features, yielding improvements in termsof desired output metrics (e.g., performance or energy consumption).2. Abstract away users from the complexity of the underlying heterogeneous hardware, delegatingthe proper exploitation of expanded scheduling choices to a system software component(typically referred as a runtime). This piece of software, armed with knowledge fromstatic architectural characteristics and dynamic status of the hardware at execution time,will exploit those combinations considered optimal among those relaxations proposed bythe user for each task ready for execution.3. Extend this abstraction in order to describe both computing systems, by means of executor/ allocator hierarchies that describe the heterogeneous computing architecture, and applications,in terms of sets of interdependent tasks. In addition, the relations between executorsand tasks are categorized into a new task-executor taxonomy, which motivates ambiguityfreeHPC programming frontends based on the STSE, Single Task - Single Executor classification,distinguished from fully-automated runtime backends.4. Propose a new programming model (STEEL) based on previous ideas, that gathers featuresconsidered to be basic for future task-based programming models, namely: performance,composability, expressivity and hard-to-misuse interfaces.5. Specify an API to support the STEEL programming model, and a runtime implementationleveraging techniques and programming paradigms supported by modern C++, illustratingits flexibility, ease of use and performance impact by means of simple use cases and examples.Hence, the proposed methodology stands for a clear and strict separation of concerns betweenthe involved actors in a parallel executions: user / codes and underlying hardware. This kind ofabstractions allows a delegation of the expert knowledge from the user toward the system software(runtime) in a systematic way, and facilitates the integration of mechanisms to automate optimizations,adapting performance to the specificities of the heterogeneous parallel architecture in whichthe code is instantiated and executed.From this perspective, the thesis designs, implements and validates mechanisms to perform aso-called complexity formalization, classifying many actions that are currently done by the userand building a framework in which these complexities can be delegated to the runtime system. Thedelegation of these decisions is already a step forward to next generation of programming modelsseeking performance, expressivity, programmability and portability...La presente tesis doctoral propone el diseño e implementación de un nuevo modelo de programación basado en relajaciones de ejecución y enfocado al ámbito de la Computación Paralela de Altas Prestaciones. Concretamente, los objetivos principales de la tesis son:1. Abogar por una metodología de desarrollo en la que el usuario define las unidades básicas de computo (tareas), junto con un conjunto de relajaciones en, posiblemente, múltiples dimensiones. Estas relajaciones se traducirán, en tiempo de ejecución, en oportunidades expandidas(y complejas) de planificación en función de la arquitectura subyacente, impactando así en métricas como rendimiento o consumo energético.2. Abstraer al usuario de la complejidad del hardware subyacente, delegando la correcta explotación de dichas posibilidades de planificación expandidas a un componente software de sistema (típicamente conocido como runtime). Dicho software, dotado de conocimiento tanto de las características estáticas de la arquitectura subyacente como del estado puntual de la misma en el momento de la ejecución, explotará las combinaciones consideradas optimas de entre las relajaciones propuestas por el usuario para cada tarea lista para set ejecutada.3. Extender dicha abstracción para describir tanto sistemas de cómputo, en forma de jerarquía de ejecutores y alojadores de memoria que en ´ultimo término describen una arquitectura de cómputo heterogénea, como aplicaciones, en forma de un conjunto de tareas interrelacionadas. Además, las relaciones entre ejecutores y tareas son clasificadas en una nueva taxonomía tarea-ejecutor, la cual motiva frontends de programación HPC sin ambigüedad basados en la clasificación STSE, Single Task - Single Executor, separada de backends runtime totalmente automatizados.4. Proponer un nuevo modelo de programación (STEEL) basado en la clasificación STSE que aglutine ciertas características consideradas básicas de cara al éxito de los futuros modelos de programación basados en tareas: rendimiento, facilidad de composición, expresividad e interfaces no permisivos ante fallos.5. Especificar una API que dé soporte al modelo de programación, así como una implementación runtime del mismo aprovechando técnicas y paradigmas soportados en el lenguaje C++ de última generación, e ilustrar su uso, flexibilidad e impacto en el rendimiento a través de ejemplos y casos de uso sencillos .La metodología que se propugna aboga por una clara y estricta separación de conceptos entre los actores básicos que componen una ejecución paralela: usuario / código y hardware subyacente. Este tipo de abstracciones permite delegar el conocimiento experto desde el usuario hacia el software de sistema, proporcionando así mecanismos para mecanizar y automatizar su optimización ,y adaptar su rendimiento a la arquitectura paralela sobre la que se instanciarán los códigos. Desde este punto de vista, la tesis diseña, implementa y valida mecanismos para llevar a cabo una formalización de la complejidad inherente a la programación paralela heterogénea, clasificando aquellas acciones que en la actualidad se llevan a cabo por parte del usuario en el proceso de desarrollo y optimización de código, y proporcionando un marco de trabajo en el que dicha complejidad puede ser delegada, de forma eficiente y consistente, a un runtime...Fac. de InformáticaTRUEunpu

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available