Detection of Silent Data Corruption in Adaptive Numerical Integration Solvers

Scientific computing requires trust in results. In high-performance computing, trust is impeded by silent data corruption (SDC), in other words corruption that remains unnoticed. Numerical integration solvers are especially sensitive to SDCs because an SDC introduced in a certain step affects all the following steps. SDCs can even cause the solver to become unstable. Adaptive solvers can change the step size, by comparing an estimation of the approximation error with an user-defined tolerance. If the estimation exceeds the tolerance, the step is rejected and recomputed. Adaptive solvers have an inherent resilience, because some SDCs might have no consequences on the accuracy of the results, and some SDCs might push the approximation error beyond the tolerance. Our first contribution shows that the rejection mechanism is not reliable enough to reject all SDCs that affect the results' accuracy, because the estimation is also corrupted. We therefore provide another protection mechanism: at the end of each step, a second error estimation is employed to increase the redundancy. Because of the complex dynamics, the choice of the second estimate is difficult: two methods are explored. We evaluated them in HyPar and PETSc, on a cluster of 4,096 cores. We injected SDCs that are large enough to affect the trust or the convergence of the solvers. The new approach can detect 99% of the SDCs, reducing by more than 10 times the number of undetected SDCs. Compared with replication, a classic SDC detector, our protection mechanism reduces the memory overhead by more than 2 times and the computational overhead by more than 20 times in our experiments.