Challenges of machine learning and mathematical modeling

The article considers the challenges and problems of machine learning that arise in supercomputer mathematical modeling of real-world processes and phenomena. Currently, such modeling has become the main tool for obtaining fundamental and applied knowledge, as well as a condition for a significant increase in labor productivity and gross domestic product. The principles of modern predictive modeling based on high-performance computing, artificial intelligence and big data processing are described. The trends in the development of high-tech mathematical and software within the framework of integrated computing environments are analyzed; the latter imply a flexible expansion of the composition of the studied models and applied algorithms, the effective use of external products, adaptation to the evolution of computer platforms focused on a long life cycle. The methodology of machine learning based on the technological cycle is presented, which includes the formation and modification of models, the implementation of a computational experiment with the solution of direct and inverse problems, analysis of the results and decision-making on optimizing activities to achieve the goals.