Search result: Catalogue data in Spring Semester 2021

Computational Science and Engineering Bachelor Information
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Fields of Specialization
Astrophysics
NumberTitleTypeECTSHoursLecturers
402-0394-00LTheoretical Cosmology
Special Students UZH must book the module AST513 directly at UZH.
W10 credits4V + 2UL. M. Mayer, J. Yoo
AbstractThis is the second of a two course series which starts with "General Relativity" and continues in the spring with "Theoretical Astrophysics and Cosmology", where the focus will be on applying general relativity to cosmology as well as developing the modern theory of structure formation in a cold dark matter Universe.
ObjectiveLearning the fundamentals of modern physical cosmology. This
entails understanding the physical principles behind the description
of the homogeneous Universe on large scales in the first part of the
course, and moving on to the inhomogeneous Universe model where
perturbation theory is used to study the development of structure
through gravitational instability in the second part of the course.
Modern notions of dark matter and dark energy will also be introduced and discussed.
ContentThe course will cover the following topics:
- Homogeneous cosmology
- Thermal history of the universe, recombination, baryogenesis and nucleosynthesis
- Dark matter and Dark Energy
- Inflation
- Perturbation theory: Relativistic and Newtonian
- Model of structure formation and initial conditions from Inflation
- Cosmic microwave background anisotropies
- Spherical collapse and galaxy formation
- Large scale structure and cosmological probes
Lecture notesIn 2021, the lectures will be live-streamed online at ETH from the Room HPV G5 at the lecture hours. The recordings will be available at the ETH website. The detailed information will be provided by the course website and the SLACK channel.
LiteratureSuggested textbooks:
H.Mo, F. Van den Bosch, S. White: Galaxy Formation and Evolution
S. Carroll: Space-Time and Geometry: An Introduction to General Relativity
S. Dodelson: Modern Cosmology
Secondary textbooks:
S. Weinberg: Gravitation and Cosmology
V. Mukhanov: Physical Foundations of Cosmology
E. W. Kolb and M. S. Turner: The Early Universe
N. Straumann: General relativity with applications to astrophysics
A. Liddle and D. Lyth: Cosmological Inflation and Large Scale Structure
Prerequisites / NoticeKnowledge of General Relativity is recommended.
Physics of the Atmosphere
NumberTitleTypeECTSHoursLecturers
701-1216-00LNumerical Modelling of Weather and Climate Information W4 credits3GC. Schär, J. Vergara Temprado, M. Wild
AbstractThe course provides an introduction to weather and climate models. It discusses how these models are built addressing both the dynamical core and the physical parameterizations, and it provides an overview of how these models are used in numerical weather prediction and climate research. As a tutorial, students conduct a term project and build a simple atmospheric model using the language PYTHON.
ObjectiveAt the end of this course, students understand how weather and climate models are formulated from the governing physical principles, and how they are used for climate and weather prediction purposes.
ContentThe course provides an introduction into the following themes: numerical methods (finite differences and spectral methods); adiabatic formulation of atmospheric models (vertical coordinates, hydrostatic approximation); parameterization of physical processes (e.g. clouds, convection, boundary layer, radiation); atmospheric data assimilation and weather prediction; predictability (chaos-theory, ensemble methods); climate models (coupled atmospheric, oceanic and biogeochemical models); climate prediction. Hands-on experience with simple models will be acquired in the tutorials.
Lecture notesSlides and lecture notes will be made available at
Link
LiteratureList of literature will be provided.
Prerequisites / NoticePrerequisites: to follow this course, you need some basic background in atmospheric science, numerical methods (e.g., "Numerische Methoden in der Umweltphysik", 701-0461-00L) as well as experience in programming. Previous experience with PYTHON is useful but not required.
Chemistry
NumberTitleTypeECTSHoursLecturers
529-0474-00LQuantum ChemistryW6 credits3GM. Reiher, T. Weymuth
AbstractIntroduction into the basic concepts of electronic structure theory and into numerical methods of quantum chemistry. Exercise classes are designed to deepen the theory; practical case studies using quantum chemical software to provide a 'hands-on' expertise in applying these methods.
ObjectiveNowadays, chemical research can be carried out in silico, an intellectual achievement for which Pople and Kohn have been awarded the Nobel prize of the year 1998. This lecture shows how that has been accomplished. It works out the many-particle theory of many-electron systems (atoms and molecules) and discusses its implementation into computer programs. A complete picture of quantum chemistry shall be provided that will allow students to carry out such calculations on molecules (for accompanying experimental work in the wet lab or as a basis for further study of the theory).
ContentBasic concepts of many-particle quantum mechanics. Derivation of the many-electron theory for atoms and molecules; starting with the harmonic approximation for the nuclear problem and with Hartree-Fock theory for the electronic problem to Moeller-Plesset perturbation theory and configuration interaction and to coupled cluster and multi-configurational approaches. Density functional theory. Case studies using quantum mechanical software.
Lecture notesHand-outs in German will be provided for each lecture (they are supplemented by (computer) examples that continuously illustrate how the theory works).

All information regarding this course, including links to the online streaming, will be available on this web page:
Link
LiteratureTextbooks on Quantum Chemistry:
F.L. Pilar, Elementary Quantum Chemistry, Dover Publications
I.N. Levine, Quantum Chemistry, Prentice Hall

Hartree-Fock in basis set representation:
A. Szabo and N. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, McGraw-Hill

Textbooks on Computational Chemistry:
F. Jensen, Introduction to Computational Chemistry, John Wiley & Sons
C.J. Cramer, Essentials of Computational Chemistry, John Wiley & Sons
Prerequisites / NoticeBasic knowledge in quantum mechanics (e.g. through course physical chemistry III - quantum mechanics) required
227-0161-00LMolecular and Materials Modelling Information W4 credits2V + 2UD. Passerone, C. Pignedoli
AbstractThe course introduces the basic techniques to interpret experiments with contemporary atomistic simulation, including force fields or ab initio based molecular dynamics and Monte Carlo. Structural and electronic properties will be simulated hands-on for realistic systems.
The modern methods of "big data" analysis applied to the screening of chemical structures will be introduced with examples.
ObjectiveThe ability to select a suitable atomistic approach to model a nanoscale system, and to employ a simulation package to compute quantities providing a theoretically sound explanation of a given experiment. This includes knowledge of empirical force fields and insight in electronic structure theory, in particular density functional theory (DFT). Understanding the advantages of Monte Carlo and molecular dynamics (MD), and how these simulation methods can be used to compute various static and dynamic material properties. Basic understanding on how to simulate different spectroscopies (IR, X-ray, UV/VIS). Performing a basic computational experiment: interpreting the experimental input, choosing theory level and model approximations, performing the calculations, collecting and representing the results, discussing the comparison to the experiment.
Content-Classical force fields in molecular and condensed phase systems
-Methods for finding stationary states in a potential energy surface
-Monte Carlo techniques applied to nanoscience
-Classical molecular dynamics: extracting quantities and relating to experimentally accessible properties
-From molecular orbital theory to quantum chemistry: chemical reactions
-Condensed phase systems: from periodicity to band structure
-Larger scale systems and their electronic properties: density functional theory and its approximations
-Advanced molecular dynamics: Correlation functions and extracting free energies
-The use of Smooth Overlap of Atomic Positions (SOAP) descriptors in the evaluation of the (dis)similarity of crystalline, disordered and molecular compounds
Lecture notesA script will be made available and complemented by literature references.
LiteratureD. Frenkel and B. Smit, Understanding Molecular Simulations, Academic Press, 2002.

M. P. Allen and D.J. Tildesley, Computer Simulations of Liquids, Oxford University Press 1990.

C. J. Cramer, Essentials of Computational Chemistry. Theories and Models, Wiley 2004

G. L. Miessler, P. J. Fischer, and Donald A. Tarr, Inorganic Chemistry, Pearson 2014.

K. Huang, Statistical Mechanics, Wiley, 1987.

N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College 1976.

E. Kaxiras, Atomic and Electronic Structure of Solids, Cambridge University Press 2010.
Fluid Dynamics
NumberTitleTypeECTSHoursLecturers
151-0208-00LComputational Methods for Flow, Heat and Mass Transfer ProblemsW4 credits4GD. W. Meyer-Massetti
AbstractNumerical methods for the solution of flow, heat & mass transfer problems are presented and illustrated by analytical & computer exercises.
ObjectiveKnowledge of and practical experience with discretization and solution methods for computational fluid dynamics and heat and mass transfer problems
Content- Introduction with application examples, steps to a numerical solution
- Classification of PDEs, application examples
- Finite differences
- Finite volumes
- Method of weighted residuals, spectral methods, finite elements
- Stability analysis, consistency, convergence
- Numerical solution methods, linear solvers
The learning materials are illustrated with practical examples.
Lecture notesSlides to be completed during the lecture will be handed out.
LiteratureReferences are provided during the lecture. Notes in close agreement with the lecture material are available (in German).
Prerequisites / NoticeBasic knowledge in fluid dynamics, thermodynamics and programming (lecture: "Models, Algorithms and Data: Introduction to Computing")
Systems and Control
NumberTitleTypeECTSHoursLecturers
227-0216-00LControl Systems II Information W6 credits4GR. Smith
AbstractIntroduction to basic and advanced concepts of modern feedback control.
ObjectiveIntroduction to basic and advanced concepts of modern feedback control.
ContentThis course is designed as a direct continuation of the course "Regelsysteme" (Control Systems). The primary goal is to further familiarize students with various dynamic phenomena and their implications for the analysis and design of feedback controllers. Simplifying assumptions on the underlying plant that were made in the course "Regelsysteme" are relaxed, and advanced concepts and techniques that allow the treatment of typical industrial control problems are presented. Topics include control of systems with multiple inputs and outputs, control of uncertain systems (robustness issues), limits of achievable performance, and controller implementation issues.
Lecture notesThe slides of the lecture are available to download.
LiteratureSkogestad, Postlethwaite: Multivariable Feedback Control - Analysis and Design. Second Edition. John Wiley, 2005.
Prerequisites / NoticePrerequisites:
Control Systems or equivalent
227-0046-10LSignals and Systems IIW4 credits2V + 2UJ. Lygeros
AbstractContinuous and discrete time linear system theory, state space methods, frequency domain methods, controllability, observability, stability.
ObjectiveIntroduction to basic concepts of system theory.
ContentModeling and classification of dynamical systems.

Modeling of linear, time invariant systems by state equations. Solution of state equations by time domain and Laplace methods. Stability, controllability and observability analysis. Frequency domain description, Bode and Nyquist plots. Sampled data and discrete time systems.

Advanced topics: Nonlinear systems, chaos, discrete event systems, hybrid systems.
Lecture notesCopy of transparencies
LiteratureRecommended:
K.J. Astrom and R. Murray, "Feedback Systems: An Introduction for Scientists and Engineers", Princeton University Press 2009

Link
Robotics
NumberTitleTypeECTSHoursLecturers
151-0854-00LAutonomous Mobile Robots Information W5 credits4GR. Siegwart, M. Chli, N. Lawrance
AbstractThe objective of this course is to provide the basics required to develop autonomous mobile robots and systems. Main emphasis is put on mobile robot locomotion and kinematics, environment perception, and probabilistic environment modeling, localizatoin, mapping and navigation. Theory will be deepened by exercises with small mobile robots and discussed accross application examples.
ObjectiveThe objective of this course is to provide the basics required to develop autonomous mobile robots and systems. Main emphasis is put on mobile robot locomotion and kinematics, environment perception, and probabilistic environment modeling, localizatoin, mapping and navigation.
Lecture notesThis lecture is enhanced by around 30 small videos introducing the core topics, and multiple-choice questions for continuous self-evaluation. It is developed along the TORQUE (Tiny, Open-with-Restrictions courses focused on QUality and Effectiveness) concept, which is ETH's response to the popular MOOC (Massive Open Online Course) concept.
LiteratureThis lecture is based on the Textbook:
Introduction to Autonomous Mobile Robots
Roland Siegwart, Illah Nourbakhsh, Davide Scaramuzza, The MIT Press, Second Edition 2011, ISBN: 978-0262015356
151-0566-00LRecursive Estimation Information W4 credits2V + 1UR. D'Andrea
AbstractEstimation of the state of a dynamic system based on a model and observations in a computationally efficient way.
ObjectiveLearn the basic recursive estimation methods and their underlying principles.
ContentIntroduction to state estimation; probability review; Bayes' theorem; Bayesian tracking; extracting estimates from probability distributions; Kalman filter; extended Kalman filter; particle filter; observer-based control and the separation principle.
Lecture notesLecture notes available on course website: Link
Prerequisites / NoticeRequirements: Introductory probability theory and matrix-vector algebra.
252-0579-00L3D Vision Information W5 credits3G + 1AM. Pollefeys, V. Larsson
AbstractThe course covers camera models and calibration, feature tracking and matching, camera motion estimation via simultaneous localization and mapping (SLAM) and visual odometry (VO), epipolar and mult-view geometry, structure-from-motion, (multi-view) stereo, augmented reality, and image-based (re-)localization.
ObjectiveAfter attending this course, students will:
1. understand the core concepts for recovering 3D shape of objects and scenes from images and video.
2. be able to implement basic systems for vision-based robotics and simple virtual/augmented reality applications.
3. have a good overview over the current state-of-the art in 3D vision.
4. be able to critically analyze and asses current research in this area.
ContentThe goal of this course is to teach the core techniques required for robotic and augmented reality applications: How to determine the motion of a camera and how to estimate the absolute position and orientation of a camera in the real world. This course will introduce the basic concepts of 3D Vision in the form of short lectures, followed by student presentations discussing the current state-of-the-art. The main focus of this course are student projects on 3D Vision topics, with an emphasis on robotic vision and virtual and augmented reality applications.
252-0220-00LIntroduction to Machine Learning Information Restricted registration - show details
Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact Link
W8 credits4V + 2U + 1AA. Krause, F. Yang
AbstractThe course introduces the foundations of learning and making predictions based on data.
ObjectiveThe course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project.
Content- Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent)
- Linear classification: Logistic regression (feature selection, sparsity, multi-class)
- Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor
- Neural networks (backpropagation, regularization, convolutional neural networks)
- Unsupervised learning (k-means, PCA, neural network autoencoders)
- The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference)
- Statistical decision theory (decision making based on statistical models and utility functions)
- Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions)
- Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE)
- Bayesian approaches to unsupervised learning (Gaussian mixtures, EM)
LiteratureTextbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
Prerequisites / NoticeDesigned to provide a basis for following courses:
- Advanced Machine Learning
- Deep Learning
- Probabilistic Artificial Intelligence
- Seminar "Advanced Topics in Machine Learning"
Physics
NumberTitleTypeECTSHoursLecturers
402-0812-00LComputational Statistical Physics Information W8 credits2V + 2UM. Krstic Marinkovic
AbstractComputer simulation methods in statistical physics. Classical Monte-Carlo-simulations: finite-size scaling, cluster algorithms, histogram-methods, renormalization group. Application to Boltzmann machines. Simulation of non-equilibrium systems.

Molecular dynamics simulations: long range interactions, Ewald summation, discrete elements, parallelization.
ObjectiveThe lecture will give a deeper insight into computer simulation methods in statistical physics. Thus, it is an ideal continuation of the lecture
"Introduction to Computational Physics" of the autumn semester. In the first part students learn to apply the following methods: Classical Monte Carlo-simulations, finite-size scaling, cluster algorithms, histogram-methods, renormalization group. Moreover, students learn about the application of statistical physics methods to Boltzmann machines and how to simulate non-equilibrium systems.

In the second part, students apply molecular dynamics simulation methods. This part includes long range interactions, Ewald summation and discrete elements.
ContentComputer simulation methods in statistical physics. Classical Monte-Carlo-simulations: finite-size scaling, cluster algorithms, histogram-methods, renormalization group. Application to Boltzmann machines. Simulation of non-equilibrium systems. Molecular dynamics simulations: long range interactions, Ewald summation, discrete elements, parallelization.
Lecture notesLecture notes and slides are available online and will be distributed if desired.
LiteratureLiterature recommendations and references are included in the lecture notes.
Prerequisites / NoticeSome basic knowledge about statistical physics, classical mechanics and computational methods is recommended.
402-0810-00LComputational Quantum Physics
Special Students UZH must book the module PHY522 directly at UZH.
W8 credits2V + 2UM. H. Fischer
AbstractThis course provides an introduction to simulation methods for quantum systems. Starting from the one-body problem, a special emphasis is on quantum many-body problems, where we cover both approximate methods (Hartree-Fock, density functional theory) and exact methods (exact diagonalization, matrix product states, and quantum Monte Carlo methods).
ObjectiveThrough lectures and practical programming exercises, after this course:
Students are able to describe the difficulties of quantum mechanical simulations.
Students are able to explain the strengths and weaknesses of the methods covered.
Students are able to select an appropriate method for a given problem.
Students are able to implement basic versions of all algorithms discussed.
Lecture notesA script for this lecture will be provided.
LiteratureA list of additional references will be provided in the script.
Prerequisites / NoticeA basic knowledge of quantum mechanics, numerical tools (numerical differentiation and integration, linear solvers, eigensolvers, root solvers, optimization), and a programming language (for the teaching assignments, you are free to choose your preferred one).
227-0161-00LMolecular and Materials Modelling Information W4 credits2V + 2UD. Passerone, C. Pignedoli
AbstractThe course introduces the basic techniques to interpret experiments with contemporary atomistic simulation, including force fields or ab initio based molecular dynamics and Monte Carlo. Structural and electronic properties will be simulated hands-on for realistic systems.
The modern methods of "big data" analysis applied to the screening of chemical structures will be introduced with examples.
ObjectiveThe ability to select a suitable atomistic approach to model a nanoscale system, and to employ a simulation package to compute quantities providing a theoretically sound explanation of a given experiment. This includes knowledge of empirical force fields and insight in electronic structure theory, in particular density functional theory (DFT). Understanding the advantages of Monte Carlo and molecular dynamics (MD), and how these simulation methods can be used to compute various static and dynamic material properties. Basic understanding on how to simulate different spectroscopies (IR, X-ray, UV/VIS). Performing a basic computational experiment: interpreting the experimental input, choosing theory level and model approximations, performing the calculations, collecting and representing the results, discussing the comparison to the experiment.
Content-Classical force fields in molecular and condensed phase systems
-Methods for finding stationary states in a potential energy surface
-Monte Carlo techniques applied to nanoscience
-Classical molecular dynamics: extracting quantities and relating to experimentally accessible properties
-From molecular orbital theory to quantum chemistry: chemical reactions
-Condensed phase systems: from periodicity to band structure
-Larger scale systems and their electronic properties: density functional theory and its approximations
-Advanced molecular dynamics: Correlation functions and extracting free energies
-The use of Smooth Overlap of Atomic Positions (SOAP) descriptors in the evaluation of the (dis)similarity of crystalline, disordered and molecular compounds
Lecture notesA script will be made available and complemented by literature references.
LiteratureD. Frenkel and B. Smit, Understanding Molecular Simulations, Academic Press, 2002.

M. P. Allen and D.J. Tildesley, Computer Simulations of Liquids, Oxford University Press 1990.

C. J. Cramer, Essentials of Computational Chemistry. Theories and Models, Wiley 2004

G. L. Miessler, P. J. Fischer, and Donald A. Tarr, Inorganic Chemistry, Pearson 2014.

K. Huang, Statistical Mechanics, Wiley, 1987.

N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College 1976.

E. Kaxiras, Atomic and Electronic Structure of Solids, Cambridge University Press 2010.
Computational Finance
Offered in the autumn semester.
Electromagnetics
NumberTitleTypeECTSHoursLecturers
227-0707-00LOptimization Methods for EngineersW3 credits2GJ. Smajic
AbstractFirst half of the semester: Introduction to the main methods of numerical optimization with focus on stochastic methods such as genetic algorithms, evolutionary strategies, etc.
Second half of the semester: Each participant implements a selected optimizer and applies it on a problem of practical interest.
ObjectiveNumerical optimization is of increasing importance for the development of devices and for the design of numerical methods. The students shall learn to select, improve, and combine appropriate procedures for efficiently solving practical problems.
ContentTypical optimization problems and their difficulties are outlined. Well-known deterministic search strategies, combinatorial minimization, and evolutionary algorithms are presented and compared. In engineering, optimization problems are often very complex. Therefore, new techniques based on the generalization and combination of known methods are discussed. To illustrate the procedure, various problems of practical interest are presented and solved with different optimization codes.
Lecture notesPDF of a short skript (39 pages) plus the view graphs are provided
Prerequisites / NoticeLecture only in the first half of the semester, exercises in form of small projects in the second half, presentation of the results in the last week of the semester.
Geophysics
Recommended combinations:
Subject 1 + Subject 2
Subject 1 + Subject 3
Subject 2 + Subject 3
Subject 3 + Subject 4
Subject 5 + Subject 6 + Subject 8
Subject 4 + Subject 5
Subject 7 + Subject 8
Geophysics: Subject 1
offered in the autumn semester
Geophysics: Subject 2
offered in the autumn semester
Geophysics: Subject 3
NumberTitleTypeECTSHoursLecturers
651-4008-00LDynamics of the Mantle and LithosphereW3 credits2GA. Rozel
AbstractThe goal of this course is to obtain a detailed understanding of the physical properties, structure, and dynamical behavior of the mantle-lithosphere system, focusing mainly on Earth but also discussing how these processes occur differently in other terrestrial planets.
ObjectiveThe goal of this course is to obtain a detailed understanding of the physical properties, structure, and dynamical behavior of the mantle-lithosphere system, focusing mainly on Earth but also discussing how these processes occur differently in other terrestrial planets.
Geophysics: Subject 4
NumberTitleTypeECTSHoursLecturers
651-4094-00LNumerical Modelling for Applied GeophysicsW5 credits2GJ. Robertsson, H. Maurer
AbstractNumerical modelling in environmental and exploration geophysics. The course covers different numerical methods such as finite difference and finite element methods applied to solve PDE’s for instance governing seismic wave propagation and geoelectric problems.

Prerequisites include basic knowledge of (i) signal processing and applied mathematics such as Fourier analysis and (ii) Matlab.
ObjectiveAfter this course students should have a good overview of numerical modelling techniques commonly used in environmental and exploration geophysics. Students should be familiar with the basic principles of the methods and how they are used to solve real problems. They should know advantages and disadvantages as well as the limitations of the individual approaches.

The course includes exercises in Matlab where the stduents both should lear, understand and use existing scripts as well as carrying out some coding in Matlab themselves.
ContentDuring the first part of the course, the following topics are covered:
- Applications of modelling
- Physics of acoustic, elastic, viscoelastic wave equations as well as Maxwell's equations for electromagnetic wave propagation and diffusive problems
- Recap of basic techniques in signal processing and applied mathematics
- Potential field modelling
- Solving PDE's, boundary conditions and initial conditions
- Acoustic/elastic wave propagation I, explicit time-domain finite-difference methods
- Acoustic/elastic wave propagation II, Viscoelastic, pseudospectral
- Acoustic/elastic wave propagation III, spectral accuracy in time, frequency domain FD, Eikonal
- Implicit finite-difference methods (geoelectric)
- Finite element methods, 1D/2D (heat equation)
- Finite element methods, 3D (geoelectric)
- Acoustic/elastic wave propagation IV, Finite element and spectral element methods
- HPC and current challenges in computational seismology
- Seismic data imaging project

Most of the lecture modules are accompanied by exercises Small projects will be assigned to the students. They either include a programming exercise or applications of existing modelling codes.
Lecture notesPresentation slides and some background material will be provided.
LiteratureIgel, H., 2017. Computational seismology: a practical introduction. Oxford University Press.
Prerequisites / NoticeThis course is offered as a full semester course. During the second part of the semester some lecture slots will be dedicated towards working on exercises and course projects.
Geophysics: Subject 5
offered in the autumn semester
Geophysics: Subject 6
NumberTitleTypeECTSHoursLecturers
651-4006-00LSeismology of the Spherical EarthW3 credits3GM. van Driel, S. C. Stähler
AbstractBrief review of continuum mechanics and the seismic wave equation; P and S waves; reciprocity and representation theorems; eikonal equation and ray tracing; Huygens and Fresnel; surface-waves; normal-modes; seismic interferometry and noise; numerical solutions.
ObjectiveAfter taking this course, students will have the background knowledge necessary to start an original research project in quantitative seismology.
LiteratureShearer, P., Introduction to Seismology, Cambridge University Press,
1999.

Aki, K. and P. G. Richards, Quantitative Seismology, second edition,
University Science Books, Sausalito, 2002.

Nolet, G., A Breviary of Seismic Tomography, Cambridge University Press, 2008.
Prerequisites / NoticeThis is a quantitative lecture with an emphasis on mathematical description of wave propagation phenomena on the global scale, hence basic knowledge in vector calculus, linear algebra and analysis as well as seismology (e.g. from the 'wave propagation' lecture) are essential to follow this course.
Geophysics: Subject 7
NumberTitleTypeECTSHoursLecturers
651-4096-00LInverse Theory I: BasicsW3 credits2VA. Fichtner
AbstractInverse theory is the art of inferring properties of a physical system from noisy and sparse observations. It is used to transform observations of waves into 3D images of a medium seismic tomography, medical imaging and material science; to constrain density in the Earth from gravity; to obtain probabilities of life on exoplanets ... . Inverse theory is at the heart of many natural sciences.
ObjectiveThe goal of this course is to enable students to develop a mathematical formulation of specific inference (inverse) problems that may arise anywhere in the physical sciences, and to implement suitable solution methods. Furthermore, students should become aware that nearly all relevant inverse problems are ill-posed, and that their meaningful solution requires the addition of prior knowledge in the form of expertise and physical intuition. This is what makes inverse theory an art.
ContentThis first of two courses covers the basics needed to address (and hopefully solve) any kind of inverse problem. Starting from the description of information in terms of probabilities, we will derive Bayes' Theorem, which forms the mathematical foundation of modern scientific inference. This will allow us to formalise the process of gaining information about a physical system using new observations. Following the conceptual part of the course, we will focus on practical solutions of inverse problems, which will lead us to study Monte Carlo methods and the special case of least-squares inversion.

In more detail, we aim to cover the following main topics:

1. The nature of observations and physical model parameters
2. Representing information by probabilities
3. Bayes' theorem and mathematical scientific inference
4. Random walks and Monte Carlo Methods
5. The Metropolis-Hastings algorithm
6. Simulated Annealing
7. Linear inverse problems and the least-squares method
8. Resolution and the nullspace
9. Basic concepts of iterative nonlinear inversion methods

While the concepts introduced in this course are universal, they will be illustrated with numerous simple and intuitive examples. These will be complemented with a collection of computer and programming exercises.

Prerequisites for this course include (i) basic knowledge of analysis and linear algebra, (ii) basic programming skills, for instance in Matlab or Python, and (iii) scientific curiosity.
Lecture notesPresentation slides and detailed lecture notes will be provided.
Prerequisites / NoticeThis course is offered as a half-semester course during the first part of the semester
651-4096-02LInverse Theory II: Applications
Prerequisites: The successful completion of 651-4096-00L Inverse Theory I: Basics is mandatory.
W3 credits2GA. Fichtner, C. Böhm
AbstractThis second part of the course on Inverse Theory provides an introduction to the numerical solution of large-scale inverse problems. Specific examples are drawn from different areas of geophysics and image processing. Students solve various model problems using python and jupyter notebooks, and familiarize themselves with relevant open-source libraries and commercial software.
ObjectiveThis course provides numerical tools and recipes to solve (non)-linear inverse problems arising in nearly all fields of science and engineering. After successful completion of the class, the students will have a thorough understanding of suitable solution algorithms, common challenges and possible mitigations to infer parameters that govern large-scale physical systems from sparse data measurements.

Prerequisites for this course are (i) 651-4096-00L Inverse Theory: Basics, (ii) basic programming skills.
ContentThe class discusses several important concepts to solve (non)-linear inverse problems and demonstrates how to apply them to real-world data applications. All sessions are split into a lecture part in the first half, followed by tutorials using python and jupyter notebooks in the second. The range of covered topics include:

1. Regularization filters and image deblurring
2. Travel-time tomography
3. Line-search methods
4. Time reversal and Born’s approximation
5. Adjoint methods
6. Full-waveform inversion
Lecture notesPresentation slides and some background material will be provided.
Prerequisites / NoticeThis course is offered as a half-semester course during the second part of the semester
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