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We consider large-scale implicit solvers for the numerical solution of partial differential equations (PDEs). The solvers require the high-bandwith networks of an HPC system for a fast time to solution. The increasing variability in performance of the HPC systems, most likely caused by variable communication latencies and network congestion, however, makes the execution time of solver algorithms unpredictable and hard to measure. In particular, the performance variability of the underlying system makes the reliable comparison of different algorithms and implementations difficult or impossible on HPC. We propose the use of statistical methods relying on hidden Markov models (HMM) to separate variable performance data into regimes corresponding to different levels of system latency. This allows us to, for ex- ample, identify and remove time periods when extremely high system latencies throttle application performance and distort performance measurements. We apply HMM to the careful analysis of implicit conjugate gradient solvers for finite-element discretized PDE, in particular comparing several new communication hiding methods for matrix-free operators of a PDE, which are critical for achieving peak performance in state-of-the-art PDE solvers. The HMM analysis allows us to overcome the strong performance variability in the HPC system. Our performance results for a model PDE problem discretized with 135 million degrees of freedom parallelized over 7168 cores of the Anvil supercomputer demonstrate that the communication hiding techniques can achieve up to a 10% speedup for the matrix-free matrix-vector product. 

Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless compression, no theoretical or data-based quantification of lossy compressibility exists for scientific data. Users rely on trial and error to assess lossy compression performance. As a strong data-driven effort toward quantifying lossy compressibility of scientific datasets, we provide a statistical framework to predict compression ratios of lossy compressors. Our method is a two-step framework where (i) compressor-agnostic predictors are computed and (ii) statistical prediction models relying on these predictors are trained on observed compression ratios. Proposed predictors exploit spatial correlations and notions of entropy and lossyness via the quantized entropy. We study 8+ compressors on 6 scientific datasets and achieve a median percentage prediction error less than 12%, which is substantially smaller than that of other methods while achieving at least a 8.8× speedup for searching for a specific compression ratio and 7.8× speedup for determining the best compressor out of a collection.