Mathematical models of complex systems: theory, algorithms, applications

Description: Mathematical schemes for modeling systems. Planning simulation experiments with system models. Formalization and algorithmization of systems functioning processes. Statistical modeling of computer systems. Assessing the accuracy and reliability of modeling results. Analysis and interpretation of computer system modeling results. Modeling in research and system design. Prospects for the development of machine modeling of complex systems.

Amount of credits: 6

Пререквизиты:

• Computer modeling in Matlab

Course Workload:

Component: Component by selection

Cycle: Profiling disciplines

Goal

• Formation of theoretical knowledge on general methods and approaches to constructing mathematical models of complex systems and processes

Objective

• Developing skills and practical abilities in constructing and analyzing mathematical models of problems in various fields of knowledge
• Training in the principles of selecting methods for modeling specific problems, algorithms for detailing and synthesizing systems;

Learning outcome: knowledge and understanding

• general concepts of modeling;
• concepts and structure of an object-oriented modeling system;

Learning outcome: applying knowledge and understanding

• formulate a task, make scientifically sound decisions based on systems analysis methods and carry out experiments to verify their correctness and effectiveness;
• carry out modeling of complex technical and dynamic systems;

Learning outcome: formation of judgments

• understand the advantages and disadvantages of simulation modeling;

Learning outcome: communicative abilities

• Be proficient in the language of object-oriented modeling of dynamic systems;

Learning outcome: learning skills or learning abilities

• be able to develop methods of modeling, analysis and technology of synthesis of systems develop methods of modeling, analysis and technology of synthesis of systems in the field of engineering, technology and organizational structures.

Teaching methods

Лекции и онлайн-лекции, практические занятия с применением слайдов и других средств мультимедиа, в частности, использование платформы Open edX.

поисково-исследовательская (собственная исследовательская деятельность студентов в процессе обучения).

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Предварительные определения
• Понятие имитационного моделирования
• Концепция универсальной системы имитационного моделирования
• Моделирование случайных величин: датчики псевдослучайных чисел
• Предпосылки и ограничения
• Разработка концептуальных и блочных моделей систем
• Концепция объектно-ориентированной системы моделирования
• Математические методы моделирования систем
• Дискретно-стохастические модели
• Статистическая обработка результатов эксперимента
• Прогнозирование параметров системы
• Сложные динамические системы и их модели
• Анализ существующих подходов
• Математические модели сложной динамической системы Математические модели непрерывной системы
• Математические модели гибридного автомата

Key reading

• С. В. Звонарев. Основы математического моделирования: учебное посо бие — Екатеринбург : Изд-во Урал. ун-та, 2019. — 112 с.
• Умнов А.Е. Методы математического моделирования: Учебное пособие. – М.: МФТИ, 2022. 295 с.
• Самарский А. А., Михайлов А.П. Математическое моделирование: Идеи. Методы. Примеры. — 4-е изд., испр. — М.: Физматлит, 2021. — 320 с.

Further reading

• Бусленко, Н. П. Моделирование сложных систем -2-е изд., перераб. - М. : Наука, 1978. - 400 с.
• Павловский, Ю. Н. Имитационные модели и системы. -М. : Фазис, 2000. - 131 с
• Введение в математическое моделирование : уч. пособие / под ред. П. В. Трусова. — Москва : Университетская книга, Логос, 2007. — 440 с.