Huda Ibeid

Rio Yokota, Huda Ibeid, David Keyes

There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.

Huda Ibeid, Rio Yokota, Jennifer Pestana et al.

Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. Compared with multigrid methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.

Kazushige Goto, Huda Ibeid, Kalyan Kumaran et al.

Sustaining exascale performance in production requires engineering choices and operational practices that emerge only under real deployment constraints and demand coordination across system layers. This paper reports experience from three successive campaigns running HPL and HPL-MxP on Aurora, an Intel-based exascale system featuring the first large-scale deployment of Intel discrete GPUs, CPU-attached network interfaces, and the largest production Slingshot-11 interconnect. Aurora progressed from 0.585EF/s on 5,439 nodes to 1.01EF/s on 9,234 nodes in FP64 HPL, while HPL-MxP reached 11.64EF/s, an 11.5x speedup over FP64 enabled by mixed-precision arithmetic and Intel AMX acceleration. We identify and classify by role at production scale the system-level choices that sustained these results, including deterministic locality-aware resource mapping, explicit CPU-GPU pipelining, mixed-precision orchestration, and a hybrid P2P/collective resilience strategy introduced after synchronization stalls at scale. While some observations are Aurora-specific, the broader lessons are likely to apply to tightly coupled heterogeneous systems at extreme scale.

Huda Ibeid, Siping Meng, Oliver Dobon et al.

To understand and predict the performance of scientific applications, several analytical and machine learning approaches have been proposed, each having its advantages and disadvantages. In this paper, we propose and validate a hybrid approach for performance modeling and prediction, which combines analytical and machine learning models. The proposed hybrid model aims to minimize prediction cost while providing reasonable prediction accuracy. Our validation results show that the hybrid model is able to learn and correct the analytical models to better match the actual performance. Furthermore, the proposed hybrid model improves the prediction accuracy in comparison to pure machine learning techniques while using small training datasets, thus making it suitable for hardware and workload changes.