Publications

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Demonstrate algorithm-based resilience to silent data corruption (SDC) and hard faults in a task-based domain-decomposition preconditioner for elliptic PDEs.

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We discuss algorithm-based resilience to silent data corruption (SDC) in a task- based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDC. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ~ 51 K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamics voltage/frequency scaling, and its interplay with fault-rates, and application overhead.

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We present a resilient domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm reformulates the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to both soft and hard faults. We discuss an implementation based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Servers are assumed to be “sandboxed”, while no assumption is made on the reliability of the clients. We explore the scalability of the algorithm up to ∼12k cores, build an SST/macro skeleton to extrapolate to∼50k cores, and show the resilience under simulated hard and soft faults for a 2D linear Poisson equation.

We present a resilient domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm reformulates the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to both soft and hard faults. We discuss an implementation based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Servers are assumed to be “sandboxed”, while no assumption is made on the reliability of the clients. We explore the scalability of the algorithm up to ∼12k cores, build an SST/macro skeleton to extrapolate to∼50k cores, and show the resilience under simulated hard and soft faults for a 2D linear Poisson equation.

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We present a domain-decomposition-based pre-conditioner for the solution of partial differential equations (PDEs) that is resilient to both soft and hard faults. The algorithm is based on the following steps: first, the computational domain is split into overlapping subdomains, second, the target PDE is solved on each subdomain for sampled values of the local current boundary conditions, third, the subdomain solution samples are collected and fed into a regression step to build maps between the subdomains' boundary conditions, finally, the intersection of these maps yields the updated state at the subdomain boundaries. This reformulation allows us to recast the problem as a set of independent tasks. The implementation relies on an asynchronous server-client framework, where one or more reliable servers hold the data, while the clients ask for tasks and execute them. This framework provides resiliency to hard faults such that if a client crashes, it stops asking for work, and the servers simply distribute the work among all the other clients alive. Erroneous subdomain solves (e.g. due to soft faults) appear as corrupted data, which is either rejected if that causes a task to fail, or is seamlessly filtered out during the regression stage through a suitable noise model. Three different types of faults are modeled: hard faults modeling nodes (or clients) crashing, soft faults occurring during the communication of the tasks between server and clients, and soft faults occurring during task execution. We demonstrate the resiliency of the approach for a 2D elliptic PDE, and explore the effect of the faults at various failure rates.

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The move towards extreme-scale computing platforms challenges scientific simulations in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of communication, system faults, and requirements of low-memory usage per core. In this work, we develop a novel framework for solving PDEs via domain decomposition that reformulates the solution as a state of knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication, and is generally well-suited for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demonstrate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit flips in the binary representation of subdomain solutions.

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