Multi-modeling and multi-scale modeling as tools for solving complex real-world problems

Abstract

In previous decades a number of computational methods for calculation of very complex physical phenomena with a satisfactory accuracy have been developed. Most of these methods usually model only a single physical phenomenon, while their performance regarding accuracy and efficiency are limited within narrow spatial and temporal domains. However, solving real-world problems often requires simultaneous analysis of several coupled physical phenomena that extend over few spatial and temporal scales. Thus, in the last decade, simultaneous modeling of a number of physical phenomena (multi-modeling) and modeling across few scales (multi-scale modeling) have gained huge importance. In this paper, we give an overview of multi-modeling and multi-scale methods developed during the last decade within the Group for Scientific Computing at the Faculty of Science, University of Kragujevac. In addition, we give a short review of accompanying problems that we had to be solved in order to make the methods applicable in practice, such as parallelization of computations, parameters calibration, etc. In the first part of the paper we present methods for modeling various aspects of muscle behavior and their coupling into complex multi-models. The mechanical behavior of muscles is derived from the behavior of many individual components working together across spatial and temporal scales. Capturing the interplay between these components resulted in efficient multi-scale model. The rest of the paper is reserved for the presentation of multi-models for solving real-world problems in the field of water resources management, as well as methods for calibration of complex models' parameters. As the most illustrative example, we present methodology for solving the problem of water leakage under Visegrad dam at Drina River in Republic of Srpska. With the aim to support decision-making process during dam remediation, we have developed specialized multi-model that continuously uses the acquired observations to estimate spatial distribution of the main karst conductors, their characteristics, as well as hydraulic variables of the system.