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Facoltā di Scienze Agrarie e Alimentari Universitā degli Studi di Milano
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Modeling and simulation
Code: G570M-
Teacher:  Marco Micotti
CFU subdivision: Lectures: 4,5
Practices in classroom: 1,5
Basic aims:  The course aims to provide an overview of modeling, through the basic concepts of systems analysis, especially linear ones. It will provide the elements needed to understand how the models can be used in simulation, forecasting, planning and management, and how they can be integrated to support decision-making. During the course examples and case studies will be analyzed and the analysis will be extended to non-linear models. Computer laboratory sessions, using generic and specific software, will be provided.
Acquired skills:  Information and models role in decision-making. General knowledge on descriptive modeling. Problems and techniques for model simulation. Identification of linear parametric models. General knowledge on modeling decision-making. Some troubleshooting techniques for mathematical programming problems, even with many objectives and uncertain environmental.
Course contents:  Physical systems with mathematical models. General concepts of systems analysis: state, input and output,
balance and stability, trajectory and movement. Linear systems: representation, the study of equilibrium and stability, simulation. Identification of a model: calibration and validation of ARMAX predictors. Some
nonlinear models: cellular automa and neural networks.
The decision models: generalities and
classification. Linear programming: formulation and geometrical interpretation.
Analysis at many targets: Pareto efficiency and best compromise; Decisions in uncertain environment: selection criteria, Bayes
theorem, decision tree.
Program:  * Introduction and reminders: - the representation of reality: physical systems with mathematical models; - general concepts of systems analysis: characteristics, use and limitations of models; - Reminders of mathematics and linear algebra. * The descriptive models: - generalities and classification; - state, input and output, balance and stability, trajectory and motion. - linear systems: representation, study of equilibrium and stability. * Identification, simulation and prediction: - identification of a model: calibration and validation - simulation of a model and some examples of software; - methods of discretization of continuum models, basics of computing, dynamic error; - IN-OUT representation of linear systems, class ARMAX predictors. * Some special aspects: - cellular automa and neural networks; - analysis of data and signals: sampling and filtering. * The decision models: - generalities and classification; - linear programming: formulation and geometrical interpretation; - multi-objectives analysis: Pareto efficiency and methods of choice; - decisions in uncertain environment: selection criteria, Bayes theorem, decision tree. * Case planning and management: - discharge of pollutants; - agricultural plan of Sinai; - management of an environmental resource.
Prerequisites:  Mathematics
Preparatory instructions:  None
Learning materials:  * References: - Lecture notes. - Feature articles suggested during the course. - Exercises: G. Guariso and E. Weber, Analisi e Simulazione dei Modelli, Esculapio, Bologna, 2016. * Other useful material: - Site of prof. Guariso: https://home.deib.polimi.it/guariso/ - S. Rinaldi and C. Piccardi, I sistemi lineari: teoria, modelli, applicazioni, CittāStudi Edizioni.
Other info:  Examination is based on a written test, composed by 3 quantitative exercises on both descriptive and decisional models, 1 exercise related to laboratory activities and 4 theoretical questions.
Program of Modeling and simulation (pdf version)
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