Abstract

We present an improved adaptive approach for studying systems of ODEs affected by parameter variability and state space uncertainty. Our approach is based on a reformulation of the ODE problem as a transport problem of a probability density describing the evolution of the ensemble of systems in time. The resulting multidimensional problem is solved by representing the probability density w.r.t. an adaptively chosen Galerkin ansatz space of Gaussian distributions. Due to our improvements in adaptivity control, we substantially improved the overall performance of the original algorithm and moreover inherited the theoretical property that the number of Gaussian distribution stays constant for linear ODEs to the numerical scheme. We illustrate the approach in application to dynamical systems describing the pharmacokinetics of drugs and xenobiotics, where variability in physiological parameters is important to be considered.