Towards a simplification of models using regression trees

Abstract

Over-parametrization in modelling is a well-known issue that makes it hard to identify which part of a model is responsible for a given behaviour. In line with that ascertainment, this work presents the outline of an empirical method to simplify models by decreasing the number of parameters. By using regression trees to classify outputs according to related input parameters, the method provides the modeller with an objective tool to reduce the range of the used parameters and, under certain conditions, to establish relations between them. Thereby, the complexity of the model is reduced on the basis of mathematical arguments. As an example, a dynamic energy budget-based model of a mesopelagic bacterial ecosystem is simplified using the presented method. The main benefits of such a method are thus highlighted: (i) more robust parameter estimations; (ii) less complex formulations; and (iii) fewer modelling assumptions. To conclude, the difficulties encountered are discussed, and several solutions are proposed to deal with them.