PRISM-PSY:Precise GPU-Accelerated Parameter Synthesis for Stochastic Systems

In this paper we present PRISM-PSY, a novel tool that performs precise GPU-accelerated parameter synthesis for continuous-time Markov chains and time-bounded temporal logic specifications. We redesign, in terms of matrix-vector operations, the recently formulated algorithms for precise parameter synthesis in order to enable effective dataparallel processing, which results in significant acceleration on many-core architectures. High hardware utilisation, essential for performance and scalability, is achieved by state space and parameter space parallelisation: the former leverages a compact sparse-matrix representation, and the latter is based on an iterative decomposition of the parameter space. Our experiments on several biological and engineering case studies demonstrate an overall speedup of up to 31-fold on a single GPU compared to the sequential implementation

効率的で安全な集合間類似結合に関する研究

筑波大学 (University of Tsukuba)201

Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations

Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the Big Data era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing architectures with increasing computing power has greatly enhanced our capability to deal with a large volume of data. One the other hand, many classical, deterministic numerical linear algebra algorithms have difficulty to scale to handle large data sets. Monte Carlo methods, which are based on statistical sampling, exhibit many attractive properties in dealing with large volume of datasets, including fast approximated results, memory efficiency, reduced data accesses, natural parallelism, and inherent fault tolerance. In this dissertation, we present new Monte Carlo methods to accommodate a set of fundamental and ubiquitous large-scale linear algebra operations, including solving large-scale linear systems, constructing low-rank matrix approximation, and approximating the extreme eigenvalues/ eigenvectors, across modern distributed and parallel computing architectures. First of all, we revisit the classical Ulam-von Neumann Monte Carlo algorithm and derive the necessary and sufficient condition for its convergence. To support a broad family of linear systems, we develop Krylov subspace Monte Carlo solvers that go beyond the use of Neumann series. New algorithms used in the Krylov subspace Monte Carlo solvers include (1) a Breakdown-Free Block Conjugate Gradient algorithm to address the potential rank deficiency problem occurred in block Krylov subspace methods; (2) a Block Conjugate Gradient for Least Squares algorithm to stably approximate the least squares solutions of general linear systems; (3) a BCGLS algorithm with deflation to gain convergence acceleration; and (4) a Monte Carlo Generalized Minimal Residual algorithm based on sampling matrix-vector products to provide fast approximation of solutions. Secondly, we design a rank-revealing randomized Singular Value Decomposition (R3SVD) algorithm for adaptively constructing low-rank matrix approximations to satisfy application-specific accuracy. Thirdly, we study the block power method on Markov Chain Monte Carlo transition matrices and find that the convergence is actually depending on the number of independent vectors in the block. Correspondingly, we develop a sliding window power method to find stationary distribution, which has demonstrated success in modeling stochastic luminal Calcium release site. Fourthly, we take advantage of hybrid CPU-GPU computing platforms to accelerate the performance of the Breakdown-Free Block Conjugate Gradient algorithm and the randomized Singular Value Decomposition algorithm. Finally, we design a Gaussian variant of Freivalds’ algorithm to efficiently verify the correctness of matrix-matrix multiplication while avoiding undetectable fault patterns encountered in deterministic algorithms

Doctor of Philosophy

dissertationStochastic methods, dense free-form mapping, atlas construction, and total variation are examples of advanced image processing techniques which are robust but computationally demanding. These algorithms often require a large amount of computational power as well as massive memory bandwidth. These requirements used to be ful lled only by supercomputers. The development of heterogeneous parallel subsystems and computation-specialized devices such as Graphic Processing Units (GPUs) has brought the requisite power to commodity hardware, opening up opportunities for scientists to experiment and evaluate the in uence of these techniques on their research and practical applications. However, harnessing the processing power from modern hardware is challenging. The di fferences between multicore parallel processing systems and conventional models are signi ficant, often requiring algorithms and data structures to be redesigned signi ficantly for efficiency. It also demands in-depth knowledge about modern hardware architectures to optimize these implementations, sometimes on a per-architecture basis. The goal of this dissertation is to introduce a solution for this problem based on a 3D image processing framework, using high performance APIs at the core level to utilize parallel processing power of the GPUs. The design of the framework facilitates an efficient application development process, which does not require scientists to have extensive knowledge about GPU systems, and encourages them to harness this power to solve their computationally challenging problems. To present the development of this framework, four main problems are described, and the solutions are discussed and evaluated: (1) essential components of a general 3D image processing library: data structures and algorithms, as well as how to implement these building blocks on the GPU architecture for optimal performance; (2) an implementation of unbiased atlas construction algorithms|an illustration of how to solve a highly complex and computationally expensive algorithm using this framework; (3) an extension of the framework to account for geometry descriptors to solve registration challenges with large scale shape changes and high intensity-contrast di fferences; and (4) an out-of-core streaming model, which enables developers to implement multi-image processing techniques on commodity hardware

Doctor of Philosophy

dissertationMemory access irregularities are a major bottleneck for bandwidth limited problems on Graphics Processing Unit (GPU) architectures. GPU memory systems are designed to allow consecutive memory accesses to be coalesced into a single memory access. Noncontiguous accesses within a parallel group of threads working in lock step may cause serialized memory transfers. Irregular algorithms may have data-dependent control flow and memory access, which requires runtime information to be evaluated. Compile time methods for evaluating parallelism, such as static dependence graphs, are not capable of evaluating irregular algorithms. The goals of this dissertation are to study irregularities within the context of unstructured mesh and sparse matrix problems, analyze the impact of vectorization widths on irregularities, and present data-centric methods that improve control flow and memory access irregularity within those contexts. Reordering associative operations has often been exploited for performance gains in parallel algorithms. This dissertation presents a method for associative reordering of stencil computations over unstructured meshes that increases data reuse through caching. This novel parallelization scheme offers considerable speedups over standard methods. Vectorization widths can have significant impact on performance in vectorized computations. Although the hardware vector width is generally fixed, the logical vector width used within a computation can range from one up to the width of the computation. Significant performance differences can occur due to thread scheduling and resource limitations. This dissertation analyzes the impact of vectorization widths on dense numerical computations such as 3D dG postprocessing. It is difficult to efficiently perform dynamic updates on traditional sparse matrix formats. Explicitly controlling memory segmentation allows for in-place dynamic updates in sparse matrices. Dynamically updating the matrix without rebuilding or sorting greatly improves processing time and overall throughput. This dissertation presents a new sparse matrix format, dynamic compressed sparse row (DCSR), which allows for dynamic streaming updates to a sparse matrix. A new method for parallel sparse matrix-matrix multiplication (SpMM) that uses dynamic updates is also presented