Achieving Extreme Resolution in Numerical Cosmology Using Adaptive Mesh Refinement: Resolving Primordial Star Formation

As an entry for the 2001 Gordon Bell Award in the "special" category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code, Enzo, designed for high-resolution, multiphysics, cosmological structure formation simulations. Our parallel implementation places no limit on the depth or complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented spatial and temporal dynamic range. We report on a simulation of primordial star formation which develops over 8000 subgrids at 34 levels of refinement to achieve a local refinement of a factor of 10^12 in space and time. This allows us to resolve the properties of the first stars which form in the universe assuming standard physics and a standard cosmological model. Achieving extreme resolution requires the use of 128-bit extended precision arithmetic (EPA) to accurately specify the subgrid positions. We describe our EPA AMR implementation on the IBM SP2 Blue Horizon system at the San Diego Supercomputer Center.Comment: 23 pages, 5 figures. Peer reviewed technical paper accepted to the proceedings of Supercomputing 2001. This entry was a Gordon Bell Prize finalist. For more information visit http://www.TomAbel.com/GB

A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling

A method for incorporating multi-resolution capabilities within pre-existing global 3-D spherical mantle convection codes is presented. The method, which we term "geometric multigrid refinement", is based upon the application of a multigrid solver on non-uniform, structured grids and allows for the incorporation of local high-resolution grids within global models. Validation tests demonstrate that the method is accurate and robust, with highly efficient solutions to large-scale non-uniform problems obtained. Significantly, the scheme is conceptually simple and straightforward to implement, negating the need to reformulate and restructure large sections of code. Consequently, although more advanced techniques are under development at the frontiers of mesh refinement and solver technology research, the technique presented is capable of extending the lifetime and applicability of pre-existing global mantle convection codes

A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling

A method for incorporating multi-resolution capabilities within pre-existing global 3-D spherical mantle convection codes is presented. The method, which we term "geometric multigrid refinement", is based upon the application of a multigrid solver on non

Error Control of Iterative Linear Solvers for Integrated Groundwater Models

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a practical measure for controlling the error in rescaled linear systems. It is found that forward error can be controlled in preconditioned GMRES by rescaling the linear system and normalizing the stopping tolerance. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive-Over-Relaxation (SOR) method. Improved error control reduces redundant iterations in the GMRES algorithm and results in overall simulation speedups as large as 7.7x. This research is expected to broadly impact groundwater modelers through the demonstration of a practical approach for setting the residual tolerance in line with the solution error tolerance.Comment: 13 pages and 1 figur

Aceleración de algoritmos de procesamiento de imágenes para el análisis de partículas individuales con microscopia electrónica

Tesis Doctoral inédita cotutelada por la Masaryk University (República Checa) y la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de Lectura: 24-10-2022Cryogenic Electron Microscopy (Cryo-EM) is a vital field in current structural biology. Unlike X-ray crystallography and Nuclear Magnetic Resonance, it can be used to analyze membrane proteins and other samples with overlapping spectral peaks. However, one of the significant limitations of Cryo-EM is the computational complexity. Modern electron microscopes can produce terabytes of data per single session, from which hundreds of thousands of particles must be extracted and processed to obtain a near-atomic resolution of the original sample. Many existing software solutions use high-Performance Computing (HPC) techniques to bring these computations to the realm of practical usability. The common approach to acceleration is parallelization of the processing, but in praxis, we face many complications, such as problem decomposition, data distribution, load scheduling, balancing, and synchronization. Utilization of various accelerators further complicates the situation, as heterogeneous hardware brings additional caveats, for example, limited portability, under-utilization due to synchronization, and sub-optimal code performance due to missing specialization. This dissertation, structured as a compendium of articles, aims to improve the algorithms used in Cryo-EM, esp. the SPA (Single Particle Analysis). We focus on the single-node performance optimizations, using the techniques either available or developed in the HPC field, such as heterogeneous computing or autotuning, which potentially needs the formulation of novel algorithms. The secondary goal of the dissertation is to identify the limitations of state-of-the-art HPC techniques. Since the Cryo-EM pipeline consists of multiple distinct steps targetting different types of data, there is no single bottleneck to be solved. As such, the presented articles show a holistic approach to performance optimization. First, we give details on the GPU acceleration of the specific programs. The achieved speedup is due to the higher performance of the GPU, adjustments of the original algorithm to it, and application of the novel algorithms. More specifically, we provide implementation details of programs for movie alignment, 2D classification, and 3D reconstruction that have been sped up by order of magnitude compared to their original multi-CPU implementation or sufficiently the be used on-the-fly. In addition to these three programs, multiple other programs from an actively used, open-source software package XMIPP have been accelerated and improved. Second, we discuss our contribution to HPC in the form of autotuning. Autotuning is the ability of software to adapt to a changing environment, i.e., input or executing hardware. Towards that goal, we present cuFFTAdvisor, a tool that proposes and, through autotuning, finds the best configuration of the cuFFT library for given constraints of input size and plan settings. We also introduce a benchmark set of ten autotunable kernels for important computational problems implemented in OpenCL or CUDA, together with the introduction of complex dynamic autotuning to the KTT tool. Third, we propose an image processing framework Umpalumpa, which combines a task-based runtime system, data-centric architecture, and dynamic autotuning. The proposed framework allows for writing complex workflows which automatically use available HW resources and adjust to different HW and data but at the same time are easy to maintainThe project that gave rise to these results received the support of a fellowship from the “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/DI18/11660021. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 71367

Super-resolução em vídeos de baixa qualidade para aplicações forenses, de vigilância e móveis

Orientadores: Siome Klein Goldenstein, Anderson de Rezende RochaTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Algoritmos de super-resolução (SR) são métodos para obter um aumento da resolução de imagens compostas por pixels. Na super-resolução por múltiplas imagens, um conjunto de imagens de baixa resolução de uma cena é combinado para construir uma imagem de resolução superior. Super-resolução é uma solução barata para superar as limitações dos sistemas de aquisição de imagens, e pode ser útil em diversos casos em que o dispositivo não pode ser melhorado ou substituído - mas em que é possível obter diversas capturas da mesma cena. Neste trabalho, é explorada a super-resolução por múltiplas imagens para imagens naturais, em cenários nos quais é possível obter diversas imagens de uma cena. São propostas cinco variações de um método que explora propriedades geométricas de múltiplas imagens de baixa resolução para combiná-las em uma imagem de resolução superior; duas variações de um método que combina técnicas de inpainting e super-resolução; e mais três variações de um método que utiliza filtros adaptativos e regularização para resolver um problema de mínimos quadrados. Super-resolução por múltiplas imagens é possível quando existe movimento e informações não redundantes entre as imagens de baixa resolução. Entretanto, combiná-las em uma imagem de resolução superior pode não ser computacionalmente viável por técnicas complexas de super-resolução. A primeira aplicação dos métodos propostos é para um conjunto de imagens capturadas pelos dispositivos móveis mais recentes. Este tipo de ambiente requer algoritmos eficazes que sejam executados rapidamente e utilizando baixo consumo de memória. A segunda aplicação é na Ciência Forense. Câmeras de vigilância espalhadas pelas cidades poderiam fornecer dicas importantes para identificar um suspeito, por exemplo, em uma cena de crime. Entretanto, o reconhecimento dos caracteres de placas veiculares é especialmente difícil quando a resolução das imagens é baixa. Por isso, este trabalho também propõe um arcabouço que realiza a super-resolução de placas veiculares em vídeos reais de vigilância, capturados por câmeras de baixa qualidade e não projetadas especificamente para esta tarefa, ajudando o especialista forense a compreender um evento de interesse. O arcabouço realiza todas as etapas necessárias para rastrear, alinhar, reconstruir e reconhecer automaticamente os caracteres de uma placa suspeita. O usuário recebe, como saída, a imagem de alta resolução reconstruída, mais rica em detalhes, e também a sequência de caracteres reconhecida automaticamente nesta imagem. São apresentadas validações quantitativas e qualitativas dos algoritmos propostos e de suas aplicações. Os experimentos mostram, por exemplo, que é possível aumentar o número de caracteres reconhecidos corretamente, colocando o arcabouço proposto como uma ferramenta importante para fornecer aos peritos uma solução para o reconhecimento de placas veiculares sob condições adversas de aquisição. Por fim, também é sugerido o número mínimo de imagens a ser utilizada como entrada em cada aplicaçãoAbstract: Super-resolution (SR) algorithms are methods for achieving high-resolution (HR) enlargements of pixel-based images. In multi-frame super resolution, a set of low-resolution (LR) images of a scene are combined to construct an image with higher resolution. Super resolution is an inexpensive solution to overcome the limitations of image acquisition hardware systems, and can be useful in several cases in which the device cannot be upgraded or replaced, but multiple frames of the same scene can be obtained. In this work, we explore SR possibilities for natural images, in scenarios wherein we have multiple frames of a same scene. We design and develop five variations of an algorithm which rely on exploring geometric properties in order to combine pixels from LR observations into an HR grid; two variations of a method that combines inpainting techniques to multi-frame super resolution; and three variations of an algorithm that uses adaptive filtering and Tikhonov regularization to solve a least-square problem. Multi-frame super resolution is possible when there is motion and non-redundant information from LR observations. However, combining a large number of frames into a higher resolution image may not be computationally feasible by complex super-resolution techniques. The first application of the proposed methods is in consumer-grade photography with a setup in which several low-resolution images gathered by recent mobile devices can be combined to create a much higher resolution image. Such always-on low-power environment requires effective high-performance algorithms, that run fastly and with a low-memory footprint. The second application is in Digital Forensic, with a setup in which low-quality surveillance cameras throughout the cities could provide important cues to identify a suspect vehicle, for example, in a crime scene. However, license-plate recognition is especially difficult under poor image resolutions. Hence, we design and develop a novel, free and open-source framework underpinned by SR and Automatic License-Plate Recognition (ALPR) techniques to identify license-plate characters in low-quality real-world traffic videos, captured by cameras not designed for the ALPR task, aiding forensic analysts in understanding an event of interest. The framework handles the necessary conditions to identify a target license plate, using a novel methodology to locate, track, align, super resolve, and recognize its alphanumerics. The user receives as outputs the rectified and super-resolved license-plate, richer in details, and also the sequence of license-plates characters that have been automatically recognized in the super-resolved image. We present quantitative and qualitative validations of the proposed algorithms and its applications. Our experiments show, for example, that SR can increase the number of correctly recognized characters posing the framework as an important step toward providing forensic experts and practitioners with a solution for the license-plate recognition problem under difficult acquisition conditions. Finally, we also suggest a minimum number of images to use as input in each applicationDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação1197478,146886153996/3-2015CAPESCNP

Gaussian Process Modeling for Upsampling Algorithms With Applications in Computer Vision and Computational Fluid Dynamics

Across a variety of fields, interpolation algorithms have been used to upsample lowresolution or coarse data fields. In this work, novel Gaussian Process based methodsare employed to solve a variety of upsampling problems. Specifically threeapplications are explored: coarse data prolongation in Adaptive Mesh Refinement(AMR) in the field of Computational Fluid Dynamics, accurate document imageupsampling to enhance Optical Character Recognition (OCR) accuracy, and fastand accurate Single Image Super Resolution (SISR). For AMR, a new, efficient,and “3rd order accurate” algorithm called GP-AMR is presented. Next, a novel,non-zero mean, windowed GP model is generated to upsample low resolution documentimages to generate a higher OCR accuracy, when compared to the industrystandard. Finally, a hybrid GP convolutional neural network algorithm is used togenerate a computationally efficient and high quality SISR model

Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs

Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure correction has to be solved at every time step in the dynamical core of many numerical weather prediction models, and equations of a very similar structure arise in global ocean models, subsurface flow simulations and gas and oil reservoir modelling. The elliptic solve is often the bottleneck of the forecast, and an algorithmically optimal method has to be used and implemented efficiently. Graphics Processing Units have been shown to be highly efficient for a wide range of applications in scientific computing, and recently iterative solvers have been parallelised on these architectures. We describe the GPU implementation and optimisation of a Preconditioned Conjugate Gradient (PCG) algorithm for the solution of a three dimensional anisotropic elliptic PDE for the pressure correction in NWP. Our implementation exploits the strong vertical anisotropy of the elliptic operator in the construction of a suitable preconditioner. As the algorithm is memory bound, performance can be improved significantly by reducing the amount of global memory access. We achieve this by using a matrix-free implementation which does not require explicit storage of the matrix and instead recalculates the local stencil. Global memory access can also be reduced by rewriting the algorithm using loop fusion and we show that this further reduces the runtime on the GPU. We demonstrate the performance of our matrix-free GPU code by comparing it to a sequential CPU implementation and to a matrix-explicit GPU code which uses existing libraries. The absolute performance of the algorithm for different problem sizes is quantified in terms of floating point throughput and global memory bandwidth.Comment: 18 pages, 7 figure