Performance Prediction of Explicit ODE Methods on Multi-Core Cluster Systems

When migrating a scientific application to a new HPC system, the program code usually has to be re-tuned to achieve the best possible performance. Auto-tuning techniques are a promising approach to support the portability of performance. Often, a large pool of possible implementation variants exists from which the most efficient variant needs to be selected. Ideally, auto-tuning approaches should be capable of undertaking this task in an efficient manner for a new HPC system and new characteristics of the input data by applying suitable analytic models and program transformations. In this article, we discuss a performance prediction methodology for multi-core cluster applications, which can assist this selection process by significantly reducing the selection effort compared to in-depth runtime tests. The methodology proposed is an extension of an analytical performance prediction model for shared-memory applications introduced in our previous work. Our methodology is based on the execution-cache-memory (ECM) performance model and estimations of intra-node and inter-node communication costs, which we apply to numerical solution methods for ordinary differential equations (ODEs). In particular, we investigate whether it is possible to obtain accurate performance predictions for hybrid MPI/OpenMP implementation variants in order to support the variant selection. We demonstrate that our approach is able to reliably select a set of efficient variants for a given configuration (ODE system, solver and hardware platform) and, thus, to narrow down the search space for possible later empirical tuning.