Machine Learning-Assisted Optimization of Complex Mathematical Models

Abstract

Machine learning offers new possibilities for optimizing mathematical models involving numerous parameters, nonlinear relationships, and computationally expensive objective functions. This study examines the integration of machine learning algorithms with mathematical optimization techniques to improve prediction and decision-making. It considers neural networks, surrogate modeling, Bayesian optimization, and evolutionary algorithms for exploring complex solution spaces. Potential applications include engineering design, scientific simulation, resource allocation, and parameter estimation. The study also discusses challenges related to model uncertainty, overfitting, computational efficiency, and the interpretability of optimized solutions. Combining data-driven techniques with established mathematical methods may improve optimization performance across a broad range of scientific and industrial problems