Učni načrt predmeta

Predmet:

Matematično modeliranje kompleksnih sistemov

Course:

Mathematical Modeling of Complex Systems

Študijski program in stopnja / Study programme and level	Študijska smer / Study field	Letnik / Academic year	Semester / Semester
Informacijske in komunikacijske tehnologije, 2. stopnja	Digitalna transformacija	1	2
Information and Communication Technologies, 2nd cycle	Digital Transformation	1	2

Vrsta predmeta / Course type

Izbirni / Elective

Univerzitetna koda predmeta / University course code:

IKT-615

Predavanja Lectures	Seminar Seminar	Vaje Tutorial	Klinične vaje work	Druge oblike študija	Samost. delo Individ. work	ECTS
15	15			15	105	5

*Navedena porazdelitev ur velja, če je vpisanih vsaj 15 študentov. Drugače se obseg izvedbe kontaktnih ur sorazmerno zmanjša in prenese v samostojno delo. / This distribution of hours is valid if at least 15 students are enrolled. Otherwise the contact hours are linearly reduced and transfered to individual work.

Nosilec predmeta / Course leader:

prof. dr. Đani Juričić

Sodelavci / Lecturers:

Jeziki / Languages:

Predavanja / Lectures:

slovenščina, angleščina / Slovenian, English

Vaje / Tutorial:

Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisites:

Zaključen študijski program prve stopnje s področja naravoslovja, tehnike ali računalništva.

Student must complete first-cycle study programmes in natural sciences, technical disciplines or computer science.

Vsebina:

Content (Syllabus outline):

1) Uvod:
Faze procesa sinteze modela, osnove nelinearne dinamike.
2) Kompleksna dinamika:
Modeli kompleksnih in samo-organizirajočih sistemov; determinizem, prediktabilnost in kavzalnost v (kompleksnih) dinamičnih sistemih; stohastični procesi, Fokker-Planckova enačba; sinhronizacija.
3) Analiza kompleksnih dinamičnih sistemov: Spektralne metode (Fourierjeva in valčna analiza), Lyapunov eksponent, korelacijska dimenzija.
4) Sodobni koncepti simulacije:
Osnove numerične integracije; stabilnost, konvergenca, natančnost. Simulacija sistemov diferencialno-algebrajskih enačb. Simulacija modelov s porazdeljenimi parametri; metoda končnih elementov, brezmrežne metode (s primeri iz ekologije, prevajanja toplote, Black-Scholes finančni model).
Simulacija stohastičnih sistemov (Monte Carlo pristopi, Markovske verige). Nekaj orodij za simulacijo: Matlab, Simulink, Femlab.
5) Sinteza modelov kompleksnih dinamičnih sistemov iz podatkov:
Osnove linearne regresije in metode instrumentalnih spremenljivk. Identifikacija neparametričnih modelov (nevronske mreže, Gaussovi procesi). Bayesov pristop k identifikaciji kompleksnih dinamičnih sistemov. Primeri aplikacij.

1) Uvod:
Basic steps of the model synthesis process, basics of nonlinear dynamics.
2) Complex dynamics:
Models of complex and self-organizing systems; determinism, predictability and causality in (complex) dynamic systems; stochastic processes, Fokker-Planck equation; synchronization.
3) Analysis of complex dynamic systems:
Spectral methods (Fourier and vawelet analysis), Lyapunov exponent, correlation dimension.
4) Advanced simulation:
Basics of numerical integration. Simulation of differential-algebraic equations. Simulation of models with distributed parameters; method of final elements, offline methods (with examples from ecology, heat conduction, Black-Scholes financial model).
Simulation of stochastic systems (Monte Carlo approaches, Markov chains). Simulation tools: Matlab, Simulink, Femlab.
5) Data driven modelling of complex dynamic systems:
Basics of linear regression and instrumental variables method. Nonparametric model identification (neural networks, Gaussian processes). Bayesian approach to the identification of complex dynamic systems. Applications.

Temeljna literatura in viri / Readings:

H. Sayama (2015). Introduction to the Modeling and Analysis of Complex Systems, Open SUNY Textbooks, Milne Library, Geneseo, NY.
Y.W. Kwon (2015). Multiphysics and Multiscale Modeling: Techniques and Applications. CRC Press.
L. Ljung (2016). Modeling & Identification of Dynamic Systems, Studentlitteratur AB.
J.N. Kutz (2013). Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data, Oxford University Press, Oxford.
X. Han, P. E. Kloeden (2017). Random Ordinary Differential Equations and Their Numerical Solution. Springer, Singapore.
J. Kocijan (2016). Modelling and Control of Dynamic Systems Using Gaussian Process Models, Springer. London.
S.A. Billings (2013). Nonlinear System Identification NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley, Chichester.
J. N. Kutz, S.l. Brunton, B.W. Brunton, J.l. Proctor (2016), Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. Oxford University Press, Oxford.
U. Spagnolini (2018). Statistical Signal Processing in Engineering. Wiley, Chichester.

Cilji in kompetence:

Objectives and competences:

Matematično modeliranje je izrazito generična in interdisciplinarna znanstvena veja, katere znanja se uporabljajo v domala vseh vejah naravoslovnih, tehničnih in e-znanosti. Namen predmeta je seznaniti slušatelje z izbranimi temami iz problematike sinteze modelov kompleksnih dinamičnih procesov, njihove simulacije in kalibracije. Predstavljene bodo osnovne tehnike in ideje, razpoložljiva orodja za modeliranje in simulacijo ter zgledi praktične uporabe.

Študent bo sposoben načrtovanja modelov na podlagi osnovnih fizikalnih načel in načrtovanja modelov iz podatkov.

Mathematical modelling is a distinctly generic and interdisciplinary branch of science which is applied in almost all branches of natural, technical and, last but not least, e-science. The purpose of this course is to present selected topics related to the issues of the synthesis of models for complex dynamic processes, their simulations and calibration. The presentation will include basic techniques and ideas, available modelling and simulation tools and examples of their practical use.

The student will be able to design models based on basic physical principles and design models from data.

Predvideni študijski rezultati:

Intendeded learning outcomes:

Študenti bodo z uspešno opravljenimi obveznostmi tega predmeta pridobili:
- razumevanje procesa modeliranja dinamičnih sistemov,
- sposobnost povezovanja sistemskih znanj in matematičnih orodij pri sintezi modela dinamičnega procesa,
- sposobnost uporabe teoretičnih znanj v praksi,
- delo v multidisciplinarnih skupinah,
- dokumentiranje in diseminacija rezultatov dela na mednarodnem nivoju,
- sposobnost reševanja zahtevnejših problemov modeliranja,
- razumevanje dinamike kompleksnih sistemov,
- spoznavanje osnovnih orodij za simulacijo dinamičnih sistemov.

Students successfully completing this course will acquire:
- understanding of the process modeling cycle,
- the ability to combine knowledge of systems sciences and mathematical tools in model synthesis,
- the ability to apply theoretical knowledge in practice,
- co-operation in multi-disciplinary teams,
- documentation and dissemination of results on the international level,
- ability to solve non-trivial modelling problems,
- understanding the complex systems dynamics,
- familiarity with modern simulation tools.

Metode poučevanja in učenja:

Learning and teaching methods:

Predavanja, seminarji, laboratorijsko delo.

Lectures, seminar work, laboratory work.

Načini ocenjevanja:

Delež v % / Weight in %

Assesment:

Seminar

50 %

Seminar

Ustni izpit

50 %

Oral exam

Reference nosilca / Lecturer's references:

1.	ŽNIDARIČ, Luka, JURIČIĆ, Đani, MOREL, Bertrand, GRADIŠAR, Žiga. Probabilistic electrochemical impedance spectroscopy-based fault diagnosis of solid oxide electrolysis cell systems under variable operating conditions. Applied energy. Jul. 2026, vol. 415, str. 1-18, ilustr. ISSN 1872-9118.
2.	KÖNIGSHOFER, Benjamin, HÖBER, Michael, NUSEV, Gjorgji, BOŠKOSKI, Pavle, JURIČIĆ, Đani, MARGARITIS, Nikolaos, HOCHENAUER, Christoph, SUBOTIĆ, Vanja. Towards strategies to mitigate degradation and regenerate performance of a solid oxide electrolyzer during co-electrolysis operation. Journal of power sources. 1 Feb. 2023, vol. 556, str. 1-13, ilustr. ISSN 1873-2755
3.	ŽNIDARIČ, Luka, GRADIŠAR, Žiga, JURIČIĆ, Đani. Predicting the remaining useful life of solid oxide fuel cell systems using adaptive trend models of health indicators. Energies. 2024, vol. 17, iss. 11, str. 1-20
4.	ŽNIDARIČ, Luka, NUSEV, Gjorgji, MOREL, Bertrand, MOUGIN, Julie, JURIČIĆ, Đani, BOŠKOSKI, Pavle. Evaluating uncertainties in electrochemical impedance spectra of solid oxide fuel cells. Applied energy. 2021, vol. 298, str. 117101-1-117101-14. ISSN 0306-2619
5.	NUSEV, Gjorgji, JURIČIĆ, Đani, GABERŠČEK, Miran, MOŠKON, Jože, BOŠKOSKI, Pavle. Fast impedance measurement of li-ion battery using discrete random binary excitation and wavelet transform. IEEE access. vol. 9, str. 46152-46165. ISSN 2169-3536