TY - JOUR

T1 - A New Visualization and Analysis Method for a Convolved Representation of Mass Computational Experiments with Biological Models

AU - Klimenko, Alexandra I.

AU - Vorobeva, Diana A.

AU - Lashin, Sergey A.

N1 - The study is supported by the Kurchatov Genomic Centre of the Institute of Cytology and Genetics, SB RAS (№ 075-15-2019-1662) and the Budget Project #FWNR-2022-0020 of the Ministry of Science and Higher Education of The Russian Federation.

PY - 2023/6

Y1 - 2023/6

N2 - 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.

AB - 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.

KW - computational experiment

KW - dynamic regime

KW - dynamic time warping

KW - mathematical model

KW - visualization

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85164139023&origin=inward&txGid=8e836cc06ce628b48686ee1ccc238225

UR - https://www.mendeley.com/catalogue/891594d3-23a7-3778-8dff-cb1f592d6400/

U2 - 10.3390/math11122783

DO - 10.3390/math11122783

M3 - Article

VL - 11

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 12

M1 - 2783

ER -