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

Abstract

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.

Smooth-polylines vs. polynomials in balanced identification technology: solving inverse problems of thermal conductivity

“…The choice of its values determines the quality of the solution. The choice is carried out by minimizing the root-mean-square error of cross-validation [2].…”

“…Those problems often turn out to be ill-posed and specific approaches using regularization methods are required for the solution [1]. In the balanced identification (SvF) method [2] the choice of regularization weights is making by minimizing the cross-validation error. It enables to find a balanced solution giving the optimal (in the sense of minimizing the cross-validation error) compromise between the proximity of the model to the data and the simplicity of the model [3], formalized in criterion by regularizing additive.…”

“…SvF-technology has been successfully used by solving inverse problems in various scientific fields (mechanics, plasma physics, biology, plant physiology, epidemiology, meteorology, atmospheric pollution transfer, etc., a more detailed enumeration can be found in [2]).…”

Борьба Штаммов COVID-19 В Г. Москва: Альфа, Дельта, Омикрон, Стелс (Июль 2022)

“…Использование технологии сбалансированной идентификации [4], [5] позволило построить (на основе открытых статистических данных) модель динамики эпидемии в г. Москва с учетом 4 штаммов вируса Covid-19. Полученные результаты показывают, что основным механизмом, определяющим динамику, является коллективный иммунитет и его ослабление в зависимости от времени после заболевания или прививки (соответствующие кривые можно найти в [3]).…”

Covid-19: Qualitative Change in the Behavior of the “Virus vs Human” System - From Limit Cycle to Sustained Focus

“…The considered equations do not have analytical solutions (especially since the functions b(t) and fIm(t) are the result of another study and are given numerically), therefore, numerical models approximating them, which are not given here, were studied. Let us present some of the results obtained on the basis of the balanced identification technology [3]…”