SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Inverse Problems and Modelling in Physics - NGEO076
Title in English: Obrácené úlohy a modelování ve fyzice
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Jakub Velímský, Ph.D.
Annotation -
Last update: T_KG (01.05.2013)
Model space and data space. State of information. Information obtained from physical theories. Information obtained from measurements. A priori information. Combination of experimental, a priori and theoretical information. Solution of the inverse problem. Special cases: Gaussian and generalized Gaussian hypothesis. The least-squares criterion. Trial and error method. Stochastic metods (Monte Carlo method, simulated annealing, genetic algorithm). Analysis of error and resolution.
Aim of the course -
Last update: T_KG (01.05.2013)

Understanding basic principles of inverse problem theory in physics.

Course completion requirements - Czech
Last update: RNDr. Jakub Velímský, Ph.D. (06.10.2017)

Forma zkoušky: ústní

Požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce.

Literature -
Last update: CADEK/MFF.CUNI.CZ (03.04.2008)

A. Tarantola, Inverse Problem Theory, Elsevier 1987.

http://www.ipgp.jussieu.fr/~tarantola/

Teaching methods -
Last update: RNDr. Jakub Velímský, Ph.D. (06.10.2017)

Lecture

Syllabus -
Last update: T_KG (01.05.2013)
General theory of inverse problems

Model and data spaces. State of information. Information from physical theory. Apriori information and data information. Combining the probabilities. Definition of the solution. Aposteriori information on the model space. Error analysis, resolution and stability. Special cases: Gaussian hypothesis and generalized Gaussian hypothesis.

Stochastic methods

Trial and error method. Monte Carlo. Integration by a Monte-Carlo method. Simulated annealing. Evolution strategies. Genetic algorithms.

Least-squares criterion

Methods and formulas. Analytical solution. Relaxation. Steepest descent methods. Nonlinear inverse problem. Linearisation and other techniques. Error analysis. Resolution.

 
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