The purpose of the credit module is to form the abilities of applicants for the third level of higher education (PhD) to formulate, analyze and synthesize scientific tasks in the field of information technology and system analysis at an abstract level, to critically analyze the positive and negative qualities of existing methods of system analysis, as well as to assess their possibilities for further use in solving specific scientific and practical problems, to accept scientifically based solutions in conditions of uncertainty, which requires the development of new methods, and the conduct of research and innovation activities, deep analysis and creation of new methods of data and knowledge analysis, research of weakly structured problems, development of new methods for their further use. In particular, to assimilate existing and create new methods and algorithms for approximating generalized solutions of complex nonlinear systems in special classes of spaces with nonlinear and multivalued Volterra-type mappings using recurrent neural networks using open software libraries for machine learning TensorFlow and Keras with applications to problems of approximate solution of classes of nonlinear partial derivatives with admissibly nonlinear non-monotonic differential operators of divergent type and nonlinear boundary value problems. The advantages lie in the ability to make effective approximations of solutions for problems with acceptably multivalued nonlinearities, in particular, without the uniqueness of solutions of the corresponding Cauchy problems, which is important for applications to nonlinear DRFP, nonlinear boundary value problems and control and optimization problems in infinite-dimensional spaces, and PhD students should master the following competencies: general - GC 4 Ability to independently conduct research activities, including analysis of problems, setting goals and objectives, selection of means and methods of research, as well as assessment of its quality; GC 5 Ability to initiate, plan, implement and adjust a sequential process of thorough scientific research; GC 6 Ability to critically analyze, evaluate, and synthesize new and complex ideas; GC 7 Ability for continuous self-development and self-improvement; professional – FC 1 Ability to initiate complex projects using a systematic approach and implement them independently; FC 2 Ability to comply with moral and ethical rules of conduct, research ethics, characteristics for participants in the academic environment, as well as the rules of academic integrity in scientific research; FC 3 Ability to critically analyze the positive and negative qualities of existing methods of system analysis, as well as to assess their capabilities for further use in solving specific scientific and practical problems; FC 4 Ability to make scientifically sound decisions in conditions of uncertainty, which requires the development of new methods and the conduct of research and innovation activities; FC 5 Ability to carry out research and professional activities at an interdisciplinary level; FC 6 Ability to deeply analyze and create new methods for analyzing data and knowledge; FC 7 Ability to perform research on loosely structured problems, develop new methods, and then solve them; FC 8 Ability to plan and conduct scientific research, prepare, present and publish the results of research activities. Upon completion of the course, applicants for the third level of higher education should acquire the following program learning outcomes: PRN 4 Know the advantages and disadvantages of existing methods of system analysis and the possibility of their use to solve specific scientific and applied problems in intelligent decision support systems; PRN 5 Know the basics of the organization of the research scientific process to solve significant problems in the field of system analysis, be able to apply knowledge of the basics of analysis and synthesis in various subject areas, critical comprehension and solution of research problems; PRN 10 Be able to create new methods of system analysis and mathematical models of complex systems of various nature; PRN 11 Be able to develop and use new methods for analyzing complex systems and new methods of decision-making under uncertainty; PRN 12 Be able to critically analyze the advantages and disadvantages of known methods of system analysis, as well as be able to assess the possibilities of their use to solve specific scientific and practical problems; PRN 13 Be able to develop scientific projects in the field of system analysis; PRN 14 Be able to implement the results of scientific research based on the methods of system analysis; PRN 15 Be able to solve complex problems in the field of system analysis or as a result of research and innovation activities, which involves a deep rethinking of existing and the creation of new holistic knowledge; PRN 17 Read and understand foreign texts in the specialty; freely present and discuss with specialists and non-specialists the results of research, scientific and applied problems of the industry in the state and foreign languages, competently reflect the results of research in scientific publications in leading international scientific journals; PRN 18 Adhere to the rules of academic integrity; know and adhere to the basic principles of academic integrity in scientific and educational (pedagogical) activities. Subject of study. Complex Nonlinear Systems in Special Classes of Infinite-Dimensional Distribution Spaces. The main tasks of the credit module. According to the requirements of the program of the discipline, postgraduate students after mastering the credit module must demonstrate the following learning outcomes: Knowledge: methods and tools of machine learning for the analysis of complex systems. Skills: regularization of non-smooth and multivalued nonlinearities of differential-operator equations and inclusions in special classes of distribution spaces using Yohida and Bertsekas methods. With the help of the method of artificial control, learn to justify new a priori estimates, prove new theorems on regularity and convergence for generalized solutions. For regularized tasks, investigate the topology of approximating neural networks. Develop an algorithm for the implementation of approximate solution methods using TensorFlow and Keras software libraries for machine learning. The results are to be implemented on specific test and applied problems with partial derivatives with permissible nonlinear non-monotonic differential operators of divergent type and nonlinear boundary value problems Experience: creation of a research laboratory for the analysis of complex systems (a paradigm of organized cooperation based on the experience of leading national laboratories in the United States), where the role of each team member is to specialize in a particular task in order to become the best in it, while having a holistic view of the entire process.