Toward fault-tolerant parallel-in-time integration with PFASST

We introduce and analyze different strategies for the parallel-in-time integration method PFASST to recover from hard faults and subsequent data loss. Since PFASST stores solutions at multiple time steps on different processors, information from adjacent steps can be used to recover after a processor has failed. PFASST's multi-level hierarchy allows to use the coarse level for correcting the reconstructed solution, which can help to minimize overhead. A theoretical model is devised linking overhead to the number of additional PFASST iterations required for convergence after a fault. The potential efficiency of different strategies is assessed in terms of required additional iterations for examples of diffusive and advective type

New-Sum: A Novel Online ABFT Scheme for General Iterative Methods

Emerging high-performance computing platforms, with large component counts and lower power margins, are anticipated to be more susceptible to soft errors in both logic circuits and memory subsystems. We present an online algorithm-based fault tolerance (ABFT) approach to efficiently detect and recover soft errors for general iterative methods. We design a novel checksum-based encoding scheme for matrix-vector multiplication that is resilient to both arithmetic and memory errors. Our design decouples the checksum updating process from the actual computation, and allows adaptive checksum overhead control. Building on this new encoding mechanism, we propose two online ABFT designs that can effectively recover from errors when combined with a checkpoint/rollback scheme. These designs are capable of addressing scenarios under different error rates. Our ABFT approaches apply to a wide range of iterative solvers that primarily rely on matrix-vector multiplication and vector linear operations. We evaluate our designs through comprehensive analytical and empirical analysis. Experimental evaluation on the Stampede supercomputer demonstrates the low performance overheads incurred by our two ABFT schemes for preconditioned CG (0:4% and 2:2%) and preconditioned BiCGSTAB (1:0% and 4:0%) for the largest SPD matrix from UFL Sparse Matrix Collection. The evaluation also demonstrates the exibility and effectiveness of our proposed designs for detecting and recovering various types of soft errors in general iterative methods