Toward Scalable Non-Cartesian Computing

大数据集的处理、分析和可视化是科学计算界面临的关键挑战。无论是获取的成像数据还是模拟的计算流体动力学数据集，这些数据的规模和体积都在不断增加；专家们现在正在为百亿亿次计算时代做准备，届时超级计算机将生成以艾字节（1艾字节= 10亿千兆字节）为数量级的数据集。虽然计算性能不断提高，但我们理解这种数据爆炸的认知能力肯定是不变的。由于大规模计算应用程序消耗大量的能源，我们也需要警惕环境因素。随着我们的发展，我们需要重新审视我们的数学模型和数据管理策略，以确保资源得到最佳利用。我们需要在我们可以生成的数据和我们应该生成的数据之间找到一个很好的平衡，以确保我们可以使用有限的计算和认知资源来理解数据。本提案的目标是从非笛卡尔计算的角度来解决大数据分析和可视化的挑战。非笛卡尔计算受到自然的启发，试图寻求有效的数据表示和算法来描述静态和时变的空间现象。自然界充满了这样的例子；灵长类动物视网膜上的光感受器以六角形排列，葵花籽以螺旋状的斐波那契排列，我们的皮肤细胞像一个14边的多面体，紧密地包裹着空间。然而，许多大规模计算是使用笛卡尔网格完成的，这种网格由立方单元组成，在填充空间方面效率非常低。当问题扩展到更大的规模和更高的维度时，这种低效率只会恶化。切换到非笛卡尔表示提供了一个可行且有吸引力的替代方案，因为这些表示承诺与笛卡尔对应的保真度相同-计算成本显着降低。然而，在这些表示可以用于peta和exa规模之前，需要解决可伸缩性方面的挑战。因此，本提案旨在研究专门为大规模异构计算环境设计的非笛卡尔数据管理和可视化算法。遵循“少花钱多办事”的原则，最终目标是提供简单高效的数据表示解决方案，这些解决方案可以集成到资源受限的高性能计算和可视化工作流中，而不会牺牲准确性或性能。

The processing, analysis and visualization of large datasets are key challenges faced by the scientific computing community. Be it acquired imaging data or simulated computational fluid dynamics datasets, the scale and volume of these data are on the rise; experts are now planning for the era of exascale computing where supercomputers will be generating datasets in the order of exabytes (1 exabyte = 1 billion gigabytes). While computing performance continues to improve, our cognitive ability to make sense of this data explosion is certainly constant. There are also environmental factors we need to be wary of since large-scale computing applications consume massive amounts of energy. As we go forward, we will need to revisit our mathematical models and data management strategies so as to ensure that resources are optimally utilized. We will need to find a good balance between the data we can generate and the data we should generate so as to ensure that we can make sense of the data using limited computational and cognitive resources. The goal of this proposal is to tackle large data analysis and visualization challenges from the perspective of non-Cartesian computing. Non-Cartesian computing is inspired by nature and attempts to seek efficient data representations and algorithms that describe static and time-varying spatial phenomena. Nature is replete with instances of such representations; photoreceptors in the primate retina are arranged in a hexagonal fashion, sunflower seeds are packed in a spiral Fibonacci formation and our skin cells resemble a 14-sided polytope that tightly packs space. Yet, much of large-scale computing is done using the Cartesian grid that consists of cubic cells which are very inefficient at filling space. This inefficiency only worsens as problems are scaled up to larger sizes and higher dimensions. Switching to non-Cartesian representations offers a viable and attractive alternative as these representations promise the same fidelity as their Cartesian counterparts -- with significantly less computational cost. However, there are scalability challenges that need to be addressed before these representations can be used at peta and exa scales. This proposal therefore aims to investigate non-Cartesian data management and visualization algorithms that are specially designed for large-scale heterogeneous computing environments. Following the "do more with less" mantra, the ultimate goal is to offer simple and efficient data representation solutions that can be integrated into resource-constrained high performance computing and visualization workflows without sacrificing accuracy or performance.