The main flaw of neural network ensembling is that it is exceptionally demanding computationally, especially, if the individual sub-models are large neural networks, which must be trained separately. Having in mind that modern DNNs can be very accurate, they are already the huge ensembles of simple classifiers, and that one can construct more thrifty compressed neural net of a similar performance for any ensemble, the idea of designing the expensive SuperNets can be questionable. The widespread belief that ensembling increases the prediction time, makes it not attractive and can be the reason that the main stream of ML research is directed towards developing better loss functions and learning strategies for more advanced and efficient neural networks. On the other hand, all these factors make the architectures more complex what may lead to overfitting and high computational complexity, that is, to the same flaws for which the highly parametrized SuperNets ensembles are blamed. The goal of the master thesis is to speed up the execution time required for ensemble generation. Instead of training K inaccurate sub-models, each of them can represent various phases of training (representing various local minima of the loss function) of a single DNN [Huang et al., 2017; Gripov et al., 2018]. Thus, the computational performance of the SuperNet can be comparable to the maximum CPU time spent on training its single sub-model, plus usually much shorter CPU time required for training the SuperNet coupling factors.

The concept of mathematical modeling is widespread across almost all of the fields of contemporary science and engineering. Because of the existing necessity of predictions the behavior of natural phenomena, the researchers develop more and more complex models. However, despite their ability to better forecasting, the problem of an appropriate fitting ground truth data to those, high-dimensional and nonlinear models seems to be inevitable. In order to deal with this demanding problem the entire discipline of data assimilation has been developed. Basing on the Human and Nature Dynamics (HANDY) model, we have presented a detailed and comprehensive comparison of Approximate Bayesian Computation (classic data assimilation method) and a novelty approach of Supermodeling. Furthermore, with the usage of Sensitivity Analysis, we have proposed the methodology to reduce the number of coupling coefficients between submodels and as a consequence to increase the speed of the Supermodel converging. In addition, we have demonstrated that usage of Approximate Bayesian Computation method with the knowledge about parameters' sensitivities could result with satisfactory estimation of the initial parameters. However, we have also presented the mentioned methodology as unable to achieve similar predictions to Approximate Bayesian Computation. Finally, we have proved that Supermodeling with synchronization via the most sensitive variable could effect with the better forecasting for chaotic as well as more stable systems than the Approximate Bayesian Computation. What is more, we have proposed the adequate methodologies.