Exploring the feasibility of lossy compression for PDE simulations

Abstract

Checkpoint restart plays an important role in high-performance computing (HPC) applications, allowing simulation runtime to extend beyond a single job allocation and facilitating recovery from hardware failure. Yet, as machines grow in size and in complexity, traditional approaches to checkpoint restart are becoming prohibitive. Current methods store a subset of the application's state and exploit the memory hierarchy in the machine. However, as the energy cost of data movement continues to dominate, further reductions in checkpoint size are needed. Lossy compression, which can significantly reduce checkpoint sizes, offers a potential to reduce computational cost in checkpoint restart. This article investigates the use of numerical properties of partial differential equation (PDE) simulations, such as bounds on the truncation error, to evaluate the feasibility of using lossy compression in checkpointing PDE simulations. Restart from a checkpoint with lossy compression is considered for a fail-stop error in two time-dependent HPC application codes: PlasComCM and Nek5000. Results show that error in application variables due to a restart from a lossy compressed checkpoint can be masked by the numerical error in the discretization, leading to increased efficiency in checkpoint restart without influencing overall accuracy in the simulation.

Use cases of lossy compression for floating-point data in scientific data sets

“…Sasaki et al (2015) proposed a lossy compression technique based on wavelet transformation for checkpointing and explored its impact in a production climate application. Calhoun et al (2018) verified the feasibility of using lossy compression in checkpointing two specific PDE simulations experimentally. Their results show that the compression errors in the checkpointing files can be masked by the numerical errors in the discretization, leading to improved performance without degraded overall accuracy in the simulation.…”

Improving performance of iterative methods by lossy checkponting

“…If eb is set to O(||r (t ) ||/||b ||), then eb · ||b|| is O(||r (t ) ||); hence, ||r (t ) || + eb · ||b|| is O(||r (t ) ||), which means that the new residual norm ||r ′(t ) || will be of the same order as the previous residual norm ||r (t ) || based on Equation (14). □ Thanks to error-bounded compressors such as SZ and ZFP, one can easily control the distortion of data within eb · ||x (t ) ||.…”

“…Sasaki et al [45] proposed a lossy compression technique based on wavelet transformation for checkpointing and explored its impact in a production climate application. Calhoun et al [14] verified the feasibility of using lossy compression in checkpointing two specific PDE simulations experimentally. Their results show that the compression errors in the checkpointing files can be masked by the numerical errors in the discretization, leading to improved performance without degraded overall accuracy in the simulation.…”

Compression Challenges in Large Scale Partial Differential Equation Solvers

“…In this model the only influence of lossy compression is given by the time to read/write checkpoints and to recover data structures. While a simple model for time to checkpoint is given, e.g., in [90], here we just exemplarily show the influence in Figure 11, by comparing different write/read times for checkpointing. Reducing checkpoint size by lossy compression, thus reducing T CP , T DS has a small but noticeable effect on the overall runtime.…”