# 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.

We introduce noncooperatively optimized tolerance (NOT), a game theoretic generalization of highly optimized tolerance (HOT), which we illustrate in the forest fire framework. As the number of players increases, NOT retains features of HOT, such as robustness and self-dissimilar landscapes, but also develops features of self-organized criticality. The system retains considerable robustness even as it becomes fractured, due in part to emergent cooperation between players, and at the same time exhibits increasing resilience against changes in the environment, giving rise to intermediate regimes where the system is robust to a particular distribution of adverse events, yet not very fragile to changes.