As supercomputers' complexity has grown, the traditional boundaries between processor, memory, network, and accelerators have blurred, making a homogeneous computer model, in which the overall computer system is modeled as a continuous medium with homogeneously distributed computational power, memory, and data movement transfer capabilities, an intriguing and powerful abstraction. By applying a homogeneous computer model to algorithms with a given I/O complexity, we recover from first principles, other discrete computer models, such as the roofline model, parallel computing laws, such as Amdahl's and Gustafson's laws, and phenomenological observations, such as super-linear speedup. One of the homogeneous computer model's distinctive advantages is the capability of directly linking the performance limits of an application to the physical properties of a classical computer system. Applying the homogeneous computer model to supercomputers, such as Frontier, Fugaku, and the Nvidia DGX GH200, shows that applications, such as Conjugate Gradient (CG) and Fast Fourier Transforms (FFT), are rapidly approaching the fundamental classical computational limits, where the performance of even denser systems in terms of compute and memory are fundamentally limited by the speed of light.

翻译：随着超级计算机复杂性的增长，处理器、内存、网络和加速器之间的传统界限已变得模糊，这使得一种同质化计算机模型——将整个计算机系统建模为具有均匀分布的计算能力、内存和数据传输能力的连续介质——成为引人入胜且强大的抽象概念。通过将同质化计算机模型应用于具有给定I/O复杂度的算法，我们可以从第一性原理出发推导出其他离散计算机模型（如屋顶线模型）、并行计算定律（如阿姆达尔定律和古斯塔夫森定律）以及现象学观测结果（如超线性加速）。该同质化计算机模型的独特优势之一在于能够直接将应用程序的性能极限与经典计算机系统的物理属性关联起来。将这一模型应用于Frontier、Fugaku和Nvidia DGX GH200等超级计算机，结果表明共轭梯度法和快速傅里叶变换等应用正在迅速逼近经典计算的基本极限——此时即便是计算和内存密度更高的系统，其性能也从根本上受到光速的限制。