Physical Oscillator Model for Supercomputing

A parallel program together with the parallel hardware it is running on is not only a vehicle to solve numerical problems, it is also a complex system with interesting dynamical behavior: resynchronization and desynchronization of parallel processes, propagating phases of idleness, and the peculiar effects of noise and system topology are just a few examples. We propose a physical oscillator model (POM) to describe aspects of the dynamics of interacting parallel processes. Motivated by the well-known Kuramoto Model, a process with its regular compute-communicate cycles is modeled as an oscillator which is coupled to other oscillators (processes) via an interaction potential. Instead of a simple all-to-all connectivity, we employ a sparse topology matrix mapping the communication structure and thus the inter-process dependencies of the program onto the oscillator model and propose two interaction potentials that are suitable for different scenarios in parallel computing: resource-scalable and resource-bottlenecked applications. The former are not limited by a resource bottleneck such as memory bandwidth or network contention, while the latter are. Unlike the original Kuramoto model, which has a periodic sinusoidal potential that is attractive for small angles, our characteristic potentials are always attractive for large angles and only differ in the short-distance behavior. We show that the model with appropriate potentials can mimic the propagation of delays and the synchronizing and desynchronizing behavior of scalable and bottlenecked parallel programs, respectively.