Towards resilient and energy efficient scalable Krylov solvers

Exascale computing must simultaneously address both energy efficiency and resilience as power limits impact scalability and faults are more common. Unfortunately, energy efficiency and resilience have been traditionally studied in isolation and optimizing one typically detrimentally impacts the other. To deliver the promised performance within the given power budget, exascale computing mandates a deep understanding of the interplay among energy efficiency, resilience, and scalability. In this work, we propose novel methods to analyze and optimize the costs of common resilience techniques including checkpoint-restart and forward recovery. We focus on sparse linear solvers as they are the fundamental kernels in many scientific applications. In particular, we present generalized analytical and experimental methods to analyze and quantify the time and energy costs of various recovery schemes on computer clusters, and develop and prototype performance optimization and power management strategies to improve energy efficiency. Moreover, we take a deep dive into the forward recovery that recently started to draw attention from researchers, and propose a practical matrix-aware optimization technique to reduce its recovery time. This work shows that while the time and energy costs of various resilience techniques are different, they share the common components and can be quantitatively evaluated with a generalized framework. This analysis framework can be used to guide the design of performance and energy optimization technologies. While each resilience technique has its advantages depending on the fault rate, system size, and power budget, the forward recovery can further benefit from matrix-aware optimizations for large-scale computing.