Simultaneous parameter identification and discrimination of the nonparametric structure of hybrid semi-parametric models

In this work, a hybrid semi-parametric modelling framework implemented using mixed integer linear programming (MILP) is used to extract (coupled) nonlinear ordinary differential equations (ODEs) from process data. Applied to fed-batch (bio) chemical reaction systems, unknown (or partially known) system connectivity and/or reaction kinetics are represented using a multivariate rational function (MRF) superstructure. The MRF's are embedded within an ODE framework which is used to incorporate known system model characteristics. Using derivative estimation, the ODEs are decoupled and a MILP algorithm is then used to identify appropriate constitutive model terms using sparse regression. Superstructure sparsity is promoted using a L0 - pseudo norm penalty, i.e. the cardinality of the model parameter vector, enabling the simultaneous yet decoupled identification of the parameters and model structure discrimination. Using simulated data, two case studies demonstrate a principled approach to hybrid model development, distilling unknown elements of (bio) chemical model structures from process data.