Solving random ordinary differential equations on GPU clusters using multiple levels of parallelism

Random ordinary differential equations (RODEs) perfectly describe classes of timedependent problems with stochastic disturbances that are of utmost importance in science and engineering. Both their pathwise solution concept leading to a massive amount of simulations and the form of the numerical solvers for RODEs contain high potential for efficient parallelization approaches. We analyze for the first time a high performance computing parallelization relying on GPU clusters to exploit the underlying three levels of parallelism for the example of the Kanai-Tajimi earthquake model in its RODE form. We identify four basic building blocks of the application which are valid also for general RODE scenarios. We optimized and benchmarked the implementation of the four building blocks separately to be able to select the best individual parameter settings. This allows for a comparison of the total performance of the overall application which shows excellent scaling results also on large GPU clusters. The results can be generalized to both other RODE applications and other approaches relying on a parallel, efficient generation of pseudorandom numbers or realization of the Ornstein-Uhlenbeck process.