Determining the form of ordinary differential equations using model inversion

Abstract

The model inversion approximation extracts parameters from within a nonlinear function so that they are exposed in a linear position convenient for further analysis. Experimental data can then be used to examine how the parameters vary with operating conditions. In particular, linear regression provides the selection and evaluation of the nonzero elements in linear relations between the parameters and the operating conditions. Where data is generated from an ordinary differential equation, this model inversion is used to investigate certain properties of the ode equations, such as the reliance of ode terms on external conditions, and the form of nonlinear relations of the state variables.