SubjectsSubjects(version: 964)
Course, academic year 2024/2025
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Inverse Problems and Modelling in Physics - NGEO076
Title: Obrácené úlohy a modelování ve fyzice
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: doc. RNDr. Jakub Velímský, Ph.D.
Teacher(s): doc. RNDr. Jakub Velímský, Ph.D.
Is pre-requisite for: NGEO081
Annotation -
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.
Last update: T_KG (01.05.2013)
Aim of the course -

Understanding basic principles of inverse problem theory in physics.

Last update: T_KG (01.05.2013)
Course completion requirements -

Exam type: oral or telecon.

The exam covers the topics contained in the syllabus.

Last update: Velímský Jakub, doc. RNDr., Ph.D. (24.04.2020)
Literature -

A. Tarantola, Inverse Problem Theory, Elsevier 1987.

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

Last update: Velímský Jakub, doc. RNDr., Ph.D. (24.04.2020)
Teaching methods -

Lecture

Last update: Velímský Jakub, doc. RNDr., Ph.D. (06.10.2017)
Syllabus -
General theory of inverse problems

Model and data spaces. State of information (probability density, conjuction of probabilities, non-informative state). 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.

Stochastic methods

Trial and error method. Monte Carlo. Integration by a Monte-Carlo method. Metropolis-Hastings rule and sampling methods. Simulated annealing and parallel tempering. Genetic algorithms.

Least-squares criterion

Methods and formulas. Analytical solution. Steepest descent method, Newton method. Nonlinear inverse problem. Linearisation. Conjugated gradients and variable metrics.

Backus method. Introduction to inverse problems on infinitely dimensional (functional) spaces.

Last update: Velímský Jakub, doc. RNDr., Ph.D. (24.04.2020)
 
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