Research of mathematical methods and models of long-term industrial development

The importance of the study of relevant mathematical methods and models of long-term development of the national industry is substantiated. It has been proven that causal econometric models of production are relatively simple and convenient to use in practice, as well as the most common tools for researching the long-term economic future. It was defined that the production functions, adapted to individual circumstances, proved their ability to solve the assigned tasks. However, the problem of more accurate adjustment to the features of the simulated object of research is particularly relevant in the current conditions of development of Ukraine, in the conditions of concentration of attention on certain sectors, on particular branch of industry, and in connection with the revolutionary transformations of production forces and relations, in accordance with the spread of cyber-physical technologies of the Fourth Industrial revolution.In such specific circumstances, it makes sense to ask for more sophisticated models. On the one hand, they are better, as they allow more accurate tuning of the modeled object, including by adding important factors that are outside the production system. On the other hand, they are worse because they complicate the analysis and significantly increase the number of variables needed to describe the dynamics of economic growth. In this connection, expert research methods cannot be neglected. Choosing the type of model, the range of influencing factors, possible development scenarios, etc., usually requires expert assessments (often implicit). Therefore, when analyzing long-term factors and development trends, it is important to adhere to the main methodological message of expert approaches in the construction of foresights: for long time horizons in conditions of significant uncertainty, it is appropriate to ask questions not about the calculation of the "correct future", but about the assessment of the spectrum of probable scenarios of development, expansion and rethinking its new opportunities and challenges, in particular – to avoid potentially harmful ideas and expectations, embedded in the current policy.