Abstract

This study integrates results on optimization techniques for complex numerical methods used to analyze complex scientific models. The goal is to improve structural analysis, probabilistic modeling, dynamic systems simulation, integration of multiphysical behaviors, and biological modeling. While optimizing numerical techniques is crucial for the advancement of scientific modeling applications, over-reliance on historical data may neglect emerging trends and lack of accessible data for breakthroughs in new fields. Future research should expand the scope of numerical methods investigated and analyze their effects under different conditions to further explore optimization dynamics. This will fill the gaps in these areas and improve strategies to meet the changing demands of scientific modeling, thereby enhancing the practical applications of numerical methods in various fields.