Data-driven closures for stochastic dynamical systems

We develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The proposed framework relies on estimating system-dependent conditional expectations from sample paths or experimental data, and then using such estimates to compute data-driven solutions to exact probability density function (PDF) equations. We also address the important question of whether enough useful data is being injected into the exact PDF equation for the purpose of computing an accurate numerical solution. Numerical examples are presented and discussed for prototype nonlinear dynamical systems and models of systems biology evolving from random initial states.