Fast numerical evaluation of periodic solutions for a class of nonlinear systems and its applications for parameter estimation problems

Abstract

Fast numerical evaluation of forward models is central for a broad range of inverse problems. Here we propose a method for deriving computationally efficient representations of periodic solutions of parameterized systems of nonlinear ordinary differential equations. These representations depend on parameters of the system explicitly, as quadratures of parameterized computable functions. The method applies to systems featuring both linear and nonlinear parametrization, and time-varying right-hand side. In addition, it opens possibilities to invoke scalable parallel computations and suitable function approximation schemes for numerical evaluation of solutions for various parameter values. Application of the method to the problem of parameter estimation of nonlinear ordinary differential equations is illustrated with a numerical example for the Morris–Lecar system.