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This work is based on the seminar titled ``Resiliency in Numerical AlgorithmDesign for Extreme Scale Simulations'' held March 1-6, 2020 at SchlossDagstuhl, that was attended by all the authors.  Naive versions of conventional resilience techniques will not scale to theexascale regime: with a main memory footprint of tens of Petabytes,synchronously writing checkpoint data all the way to background storage atfrequent intervals will create intolerable overheads in runtime and energyconsumption. Forecasts show that the mean time between failures could be lowerthan the time to recover from such a checkpoint, so that large calculations atscale might not make any progress if robust alternatives are not investigated.  More advanced resilience techniques must be devised. The key may lie inexploiting both advanced system features as well as specific applicationknowledge. Research will face two essential questions: (1) what are thereliability requirements for a particular computation and (2) how do we bestdesign the algorithms and software to meet these requirements? One avenue wouldbe to refine and improve on system- or application-level checkpointing androllback strategies in the case an error is detected. Developers might usefault notification interfaces and flexible runtime systems to respond to nodefailures in an application-dependent fashion. Novel numerical algorithms ormore stochastic computational approaches may be required to meet accuracyrequirements in the face of undetectable soft errors.  The goal of this Dagstuhl Seminar was to bring together a diverse group ofscientists with expertise in exascale computing to discuss novel ways to makeapplications resilient against detected and undetected faults. In particular,participants explored the role that algorithms and applications play in theholistic approach needed to tackle this challenge.

Resiliency in Numerical Algorithm Design for Extreme Scale Simulations