A New Visualization and Analysis Method for a Convolved Representation of Mass Computational Experiments with Biological Models

Alexandra I. Klimenko (), Diana A. Vorobeva and Sergey A. Lashin
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Alexandra I. Klimenko: Systems Biology Department, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Science, Lavrentiev Avenue 10, 630090 Novosibirsk, Russia
Diana A. Vorobeva: Mathematics and Mechanics Department, Novosibirsk State University, Pirogova St. 1, 630090 Novosibirsk, Russia
Sergey A. Lashin: Systems Biology Department, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Science, Lavrentiev Avenue 10, 630090 Novosibirsk, Russia

Mathematics, 2023, vol. 11, issue 12, 1-19

Abstract: Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics.

Keywords: visualization; dynamic regime; mathematical model; dynamic time warping; computational experiment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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