Proper orthogonal decomposition for parameter estimation in oscillating biological networks

Proper orthogonal decomposition (POD) is frequently applied to estimate parameters of partial differential equations. This study examines the application of the POD method in estimating the parameters of an Ordinary Differential Equation (ODE) model of stable oscillating biological networks. The mathematical model used to simulate molecular interactions in these oscillating networks is related to the Gause–Lotka–Volterra equations. The findings reveal that POD generates accurate estimates of the parameters even in the presence of experimental noise; furthermore, extrapolating biologically measured data points to a number of oscillations improves the curve fits, $C^1$ approximations, and parameter estimations.