Incorporating model identifiability into equation discovery of ODE systems

Equation discovery is a machine learning technique that tries to automate the discovery of equations from measured data. In this contribution an equation discovery system based on genetic programming was developed in order to generate mechanistic models for systems described by ordinary differential equations. A problem often encountered with automatic model generation is that overly complex models are generated that "overfit" the measured data. This issue was addressed by incorporating a model identifiability measure (expressing which fraction of the model parameters can be given a unique value given the available data) into the fitness function of the individuals. Using noisy artificially generated data for a river water quality example case, it was shown that the developed system was able to generate model equations that fitted the data well and were also fully identifiable. Correct model equations were generated when starting from a model with minimum prior knowledge but also when starting from an overly complex model. As such, it was demonstrated that the developed equation discovery system is able to generate models with optimal complexity with regard to the available data