From Measure Data to Evaluation of Models: System Modeling through Custom Galerkin-Jacobi

This work presents a method to evaluate the quality of candidate models for a given observed system in terms of fitness. Taking a candidate model, i.e. a proposed differential equation, this work uses the Galerkin method with a Jacobi/Legendre polynomial basis to approximate solve it. After, this method computes the mean square error between the approximate solution and the measure data. It ends with a relative grade for the fitness of the model to the system to enable comparisons between other possible candidates. The proposed method is intended to aid evolutionary algorithms to evolve fit models to systems based on their measure data.