Fox, Alyson | Search NASA

DOE OSTI2024

ZFP: A compressed array representation for numerical computations

HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.

Lindstrom, Peter↗

DOE OSTI2024

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault-tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show that the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. Additional linear systems are also explored, one with a more dense sparsity pattern and one that includes advection. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

97 MATHEMATICS AND COMPUTING↗