Multi-Adaptive Step Control in Surrogate Simulations of Difference Block Compositions of a Specified Order

This work is dedicated to developing adaptive procedures for managing the integration step in the numerical implementation of dynamic models described by ordinary differential equations or systems of equations. For challenging cases, effective parallel procedures for adaptive step control, utilizing surrogate simulation approaches for selecting optimal parameters, are introduced into the numerical implementations of difference compositions of block methods. The data-driven machine learning methods employed in this work enable the estimation of a set of control parameters that deliver the global extremum of a multi-criteria objective function or facilitate the formation of a Pareto front. Testing of the proposed algorithms on difficult Cauchy problems, with the possibility of varying the stiffness parameter, was conducted to compare the results of classical approaches with those of the proposed methods.