Probability-Aware Selective Protection for Sparse Iterative Solvers

With the increasing scale of high-performance computing (HPC) systems, transient bit-flip errors are now more likely than ever, posing a threat to long-running scientific applications. A substantial portion of these applications involve the simulation of partial differential equations (PDEs) modeling physical processes over discretized spatial and temporal domains, with some requiring the solving of sparse linear systems. While these applications are often paired with system-level application-agnostic resilience techniques such as checkpointing and replication, the utilization of these techniques imposes significant overhead. In this work, we present a probability-aware framework that produces low-overhead selective protection schemes for the widely used Preconditioned Conjugate Gradient (PCG) method, whose performance can heavily degrade due to error propagation through the sparse matrix-vector multiplication (SpMV) operation. Through the use of a straightforward mathematical model and an optimized machine learning model, our selective protection schemes incorporate error probability to protect only certain crucial operations. An experimental evaluation using 15 matrices from the SuiteSparse Matrix Collection demonstrates that our protection schemes effectively reduce resilience overheads, often outperforming or matching both baseline and established protection schemes across all error probabilities.