Hybrid parallel computing of minimum action method

• Our hybrid strategy is consistent with current heterogeneous HPC architecture.
• Our algorithm is general for both gradient and non-gradient dynamical systems.
• Our algorithm is more suitable for large-scale simulations to study complex systems.
• Our parallelization strategy demonstrates a good strong scaling.

In this work, we report a hybrid (MPI/OpenMP) parallelization strategy for the minimum action method recently proposed in [17]. For nonlinear dynamical systems, the minimum action method is a useful numerical tool to study the transition behavior induced by small noise and the structure of the phase space. The crucial part of the minimum action method is to minimize the Freidlin–Wentzell action functional. Due to the fact that the corresponding Euler–Lagrange equation is, in general, highly nonlinear and of high order, we solve the optimization problem directly instead of discretizing the Euler–Lagrange equation to provide a general but equivalent numerical framework. To enhance the efficiency of the minimum action method for general dynamical systems we consider parallel computing. In particular, we present a hybrid parallelization strategy based on MPI and OpenMP. Numerical results are presented to demonstrate the efficiency of the proposed parallelization strategy.