Stability-Optimized High Order Methods and Stiffness Detection for Pathwise Stiff Stochastic Differential Equations

Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit and drift-implicit integrators. Here we present a HPC-driven method for deriving high strong order methods for stochastic differential equations. Utilizing GPU-accelerated global optimization, we numerically solve a constrained optimization problem which results stability-optimized adaptive methods of strong order 1.5 for SDEs. The resulting explicit methods are shown to exhibit substantially enlarged stability regions which allows for them to solve pathwise stiff biological models orders of magnitude more efficiently than previous methods like SRIW1 and Euler-Maruyama. These methods are benchmarked on a range of semi-stiff problems and demonstrate speedups between 6x previous adaptive algorithms while showing computationally infeasibility of fixed time step integrators on some of these test equations.