The article entitled “ Effectiveness of grid and random approaches for a model parameter vector optimization” based on the studies conducted by Department of Mathematical Engineering member Prof. Dr. Ahmet Duran and Artificial Intelligence and Data Science Application and Research Center member Lect. Mehmet Tunçel was published in Journal of Computational Science.

Selection of effective initial parameter vectors is important for mathematical models having parameter vectors and differential equations in many science and engineering problems. In this paper, we propose a new mathematical method for an inverse problem of parameter vector optimization. We analyze and compare the effectiveness of grid and random approaches in hyperbox in terms of nonlinear least squares error, maximum improvement factor and number of iterations for an inverse problem in a mathematical model coming from asset flow theory. This analysis is valuable to understand the population dynamics of investors and machine learning applications. We employ Monte Carlo simulations and obtain convergence diagrams. We find that the success of the grid approach is relatively better than that of the random approach based on our simulation data set in the unconstrained optimization problem having nonlinear asset flow differential equations.

https://www.sciencedirect.com/science/article/pii/S1877750323000200