Multi-Parameter Performance Modeling using Symbolic Regression

Performance modeling is becoming critically important due to the need for design-space exploration on emerging exascale architectures. Existing modeling and prediction approaches are either restricted by a limited number of parameters, or provide extreme tradeoffs between simulation performance and modeling accuracy that are not ideal for exascale simulations. At one extreme are low-level discrete-event simulators, which provide high accuracy, but are prohibitively slow for large-scale simulations. At the opposite extreme are abstract modeling approaches that are sufficiently fast, but tend to support a limited number of parameters, while also lacking accuracy due to machine-specific behaviors that deviate from anticipated models. In this paper, we improve upon existing abstract modeling approaches by leveraging symbolic regression to automatically discover an underlying multi-parameter model of the system and application that captures difficult-to-understand behaviors. For three High Performance Computing (HPC) applications running on Vulcan, we show that symbolic regression provided modeling accuracies that were $3.5 \times, 4.6 \times$, and $6.2 \times$ better than analytical models developed using linear regression.