The Application of Machine Learning Algorithms in Mathematical Modeling

With the advent of the big data era, the application of machine learning algorithms in the field of mathematical modeling is becoming increasingly widespread, providing new ideas and methods for solving complex system problems. This article systematically explores the theoretical basis, methodological system, and practical application of machine learning algorithms in mathematical modeling. Firstly, the development history and research status of the integration of machine learning and mathematical modeling were summarized through literature review; Secondly, a complete methodology system including data preprocessing, feature engineering, model selection and optimization was constructed, with a focus on analyzing the applicability of three core algorithms: random forest, support vector machine, and neural network in mathematical modeling; Then, a systematic comparison of these three algorithms was conducted from multiple dimensions, and the experimental results were discussed in detail with practical cases; Finally, the application value of machine learning in mathematical modeling was summarized. Research has shown that machine learning algorithms can effectively compensate for the shortcomings of traditional mathematical modeling methods and demonstrate significant advantages in dealing with complex system problems that are high-dimensional, nonlinear, and have unclear mechanisms.