Improved modeling by coupling imperfect models

Most of the existing approaches for combining models representing a single real-world phenomenon into a multi-model ensemble combine the models a posteriori. Alternatively, in our method the models are coupled into a supermodel and continuously communicate during learning and prediction. The method learns a set of coupling coefficients from short past data in order to unite the different strengths of the models into a better representation of the observed phenomenon. The method is examined using the Lorenz oscillator, which is altered by introducing parameter and structural differences for creating imperfect models. The short past data is obtained by the standard oscillator, and different weight is assigned to each sample of the past data. The coupling coefficients are learned by using a quasi-Newton method and an evolutionary algorithm. We also introduce a way for reducing the supermodel, which is particularly useful for models of high complexity. The results reveal that the proposed supermodel gives a very good representation of the truth even for substantially imperfect models and short past data, which suggests that the super-modeling is promising in modeling real-world phenomena.