Improving ODE Integration on Graphics Processing Units by Reducing Thread Divergence

Abstract

Ordinary differential equations are widely used for the mathematical modeling of complex systems in biology and statistics. Since the analysis of such models needs to be performed using numerical integration, many applications can be gravely limited by the computational cost. This paper present a general-purpose integrator that runs massively parallel on graphics processing units. By minimizing thread divergence and bundling similar tasks using linear regression, execution time can be reduced by 40–80% when compared to a naive GPU implementation. Compared to a 36-core CPU implementation, a 150 fold runtime improvement is measured.