pMSz: A Distributed Parallel Algorithm for Correcting Extrema and Morse Smale Segmentations in Lossy Compression

Abstract: Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to incorrect scientific conclusions in applications such as combustion and cosmology. This paper presents a distributed and parallel algorithm for correcting topological features, specifically, piecewise linear Morse Smale segmentations (PLMSS), which decompose the domain into monotone regions labeled by their corresponding local minima and maxima. While a single GPU algorithm (MSz) exists for PLMSS correction after compression, no methodology has been developed that scales beyond a single GPU for extreme scale data. We identify the key bottleneck in scaling PLMSS correction as the parallel computation of integral paths, a communication-intensive computation that is notoriously difficult to scale. Instead of explicitly computing and correcting integral paths, our algorithm simplifies MSz by preserving steepest ascending and descending directions across all locations, thereby minimizing interprocess communication while introducing negligible additional storage overhead. With this simplified algorithm and relaxed synchronization, our method achieves over 90% parallel efficiency on 128 GPUs on the Perlmutter supercomputer for real world datasets.