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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)
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Understanding basic principles of inverse problem theory in physics. Last update: T_KG (01.05.2013)
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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)
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A. Tarantola, Inverse Problem Theory, Elsevier 1987. http://www.ipgp.jussieu.fr/~tarantola/ Last update: Velímský Jakub, doc. RNDr., Ph.D. (24.04.2020)
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Lecture Last update: Velímský Jakub, doc. RNDr., Ph.D. (06.10.2017)
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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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