Biblio

We present algorithmic techniques for parallel PDE solvers that leverage numerical smoothness properties of physics simulation to detect and correct silent data corruption within local computations. We initially model such silent hardware errors (which are of concern for extreme scale) via injected DRAM bit flips. Our mitigation approach generalizes previously developed "robust stencils" and uses modified linear algebra operations that spatially interpolate to replace large outlier values. Prototype implementations for 1D hyperbolic and 3D elliptic solvers, tested on up to 2048 cores, show that this error mitigation enables tolerating orders of magnitude higher bit-flip rates. The runtime overhead of the approach generally decreases with greater solver scale and complexity, becoming no more than a few percent in some cases. A key advantage is that silent data corruption can be handled transparently with data in cache, reducing the cost of false-positive detections compared to rollback approaches.

The increasing size and complexity of massively parallel systems (e.g. HPC systems) is making it increasingly likely that individual circuits will produce erroneous results. For this reason, novel fault tolerance approaches are increasingly needed. Prior fault tolerance approaches often rely on checkpoint-rollback based schemes. Unfortunately, such schemes are primarily limited to rare error event scenarios as the overheads of such schemes become prohibitive if faults are common. In this paper, we propose a novel approach for algorithmic correction of faulty application outputs. The key insight for this approach is that even under high error scenarios, even if the result of an algorithm is erroneous, most of it is correct. Instead of simply rolling back to the most recent checkpoint and repeating the entire segment of computation, our novel resilience approach uses algorithmic error localization and partial recomputation to efficiently correct the corrupted results. We evaluate our approach in the specific algorithmic scenario of linear algebra operations, focusing on matrix-vector multiplication (MVM) and iterative linear solvers. We develop a novel technique for localizing errors in MVM and show how to achieve partial recomputation within this algorithm, and demonstrate that this approach both improves the performance of the Conjugate Gradient solver in high error scenarios by 3x-4x and increases the probability that it completes successfully by up to 60% with parallel experiments up to 100 nodes.