Model Selection by Balanced Identification: the Interplay of Optimization and Distributed Computing

The technology of formal quantitative estimation of the conformity of mathematical models to the available dataset is presented. The main purpose of the technology is to make the model selection decision-making process easier for the researcher. The method is a combination of approaches from the areas of data analysis, optimization and distributed computing including: cross-validation and regularization methods, algebraic modeling in optimization and methods of optimization, automatic discretization of differential and integral equations, and optimization REST-services. The technology is illustrated by a demo case study. A general mathematical formulation of the method is presented. It is followed by a description of the main aspects of algorithmic and software implementation. The list of success stories of the presented approach is substantial. Nevertheless, the domain of applicability and important unresolved issues are discussed.