The summer school addresses young researchers from mathematics and engineering who are already working in the field of uncertainty quantification, stochastic partial differential equations and risk analysis or are interested in these fields. It is primarily meant for PhD students, but also Master students or PostDocs are very welcome. We encourage people from both mathematics and engineering to participate.

29. July 2024 – 01. August 2024

Uncertainty is inherent in various real-world problems and the understanding of its mathematical foundations is crucial to describe stochastic systems affected with randomness or variability. In addition, there is a need for reliable computational models capable of analyzing and quantifying uncertainty, assessing risks and supporting decision-making in view of optimal allocation of resources and risk management. In numerous practical applications, uncertainty needs to be considered already in the design phase and efficient computational approaches are essential to address complex systems. This summer school provides a platform for solid theoretical understanding, state-of-the-art methodologies and interdisciplinary applications in this exciting field.

The summer school will be on-site at ETH Zürich in Switzerland.

The registration fee is 30 €. The participation to the Apéro reception is optional and the additional fee is 30 €.

The deadline for the registration is June 30th. Registration can be done via the following form:

https://forms.gle/mxx4V1h8tnE7U5Eb9

Payments should be done before the registration deadline (June 30, 2024) by bank transfer to:

Recipient: GAMM
IBAN: DE09 3307 0024 0222 0911 00
BIC: DEUTDEDBWUP
Purpose of payment: SAMM2024 YOUR_SURNAME (Please do not forget to state this reference!)

The number of participants is limited. Your registration is completed when we have received the payment.

The registration fee includes attendance of the summer school, access to event material and coffee breaks. Please note that we are unable to provide financial support for accommodation, travel costs and meals.

• Mathematical foundations of uncertainty quantification and stochastic partial differential equations
• Numerical approximation of stochastic partial differential equations
• Computational approaches and risk analysis based on uncertainty
• Surrogate modeling, optimization and inverse problems under uncertainty
• Applications of uncertainty quantification in engineering

The summer school includes lectures from experts in the field of mathematics and computational engineering introducing theoretical foundations as well as relevant applications. The lectures will be accompanied by hands-on tutorials, which transfer the theoretical foundations into working code.

Prof. Claudia Schillings
Institute of Mathematics
Free University of Berlin, Germany

Introduction to the Bayesian Approach to Inverse Problems

The efficient treatment of uncertainties in mathematical models requires ideas and tools from various disciplines including numerical analysis, statistics, probability and computational science. In this course, we will focus on the identification of parameters through observations of the response of the system – the inverse problem. The uncertainty in the solution of the inverse problem will be described via the Bayesian approach. We will derive Bayes’ theorem in the infinite dimensional setting and discuss properties such as well-posedness, statistical estimates and connections to classical regularization methods. The second part of this course will be devoted to algorithms for the efficient approximation of the solution of the Bayesian inverse problem.

Prof. Andrea Barth
Institute of Applied Analysis and Numerical Simulation
University of Stuttgart, Germany

Introduction to Uncertainty Quantification with Sampling-Based Methods

In this Lecture I will provide an introduction to Uncertainty Quantification via Monte Carlo methods and their probabilistic foundations. A primer on the necessary limit theorems in probability theory will equip us with the foundations to define and study Monte Carlo estimators. We will see that the key to improve the — at first naive — Monte Carlo approach is Variance Reduction. After a brief overview of the most common methods for the latter, I will focus on a specific one: the multilevel Monte Carlo method. This method and its variations have an optimal asymptotic computational complexity. Low regularity assumptions make these methods applicable to wide range of uncertain problems. Examples and model problems illustrate the efficiency of the method and possible improvements.

Dr. Nora Lüthen
Department of Civil, Environmental and Geomatic Engineering
ETH Zurich, Switzerland

Surrogate modelling for UQ in Engineering

Uncertainty analyses typically require numerous function evaluations, which can become prohibitively costly for complex engineering models. To reduce computational effort, surrogate models can be used, which approximate the original model and are cheap to evaluate. We consider black-box methods, i.e., methods which do not need knowledge of the inner workings of the original model. In our lectures, we introduce the two popular surrogate modeling techniques polynomial chaos expansions and Kriging, and discuss their use in sensitivity and reliability analysis. We also explore extensions, such as the case of non-scalar output. The theory is illustrated with case studies and accompanied by practical exercises.

Dr. Nicole Aretz
Oden Institute of Computational Engineering and Sciences
University of Texas at Austin, U.S.A.

Multi-fidelity Uncertainty Quantification under budget constraints: An introduction with application to ice sheet simulations

While high-fidelity models are typically too expensive computationally to permit Monte Carlo samples, for many applications, less expensive but also less accurate low-fidelity models are readily available. Multi-Fidelity Uncertainty Quantification methods expand the Monte Carlo estimator to shift the computational burden onto the low-fidelity models while still guaranteeing an unbiased estimate. Through this exploit of the model hierarchy, they guarantee a smaller statistical error for the same computational budget. In this talk, we provide introductions to multi-fidelity UQ techniques, and demonstrate them on a continental-scale model of the Greenland ice sheet.

We suggest the following hotels:

Hotel Züri by Fassbind

Hotel Limmathof

Ibis Styles Zurich City Center

Ibis Budget Zürich Airport

Hotel Montana Zürich

easyHotel Zurich West

The summer school will take place at the main building (Hauptgebäude) of ETH Zürich located at Rämistrasse 101.

The main building can be reached easily by public transportation from Zürich main station:

1. From tramstop “Bahnhofstrasse/HB” with Tram #6 (towards Zürich Zoo) to ETH/Universitätsspital station.
2. From tramstop “Bahnhofplatz/HB” with Tram #10 (towards Zürich Flughafen) to ETH/Universitätsspital station.
3. From tramstop “Central” with Polybahn to Polyterasse ETH station.

The lectures will take place in room HG D1.1 and the Apero reception will be located at the Foyer HG D30.0065.

For questions please write an e-mail to

gamm.juniors@gmail.com

Margarita Chasapi (RWTH Aachen, Germany)

Alexander Henkes (ETH Zurich, Switzerland)

Georgia Kikis (University of Duisburg-Essen, Germany)

Hendrik Geisler (Leibniz University Hannover, Germany)

Amine Othmane (Saarland University, Germany)

Katharina Klioba (Hamburg University of Technology, Germany)

Sahir Butt (Ruhr University Bochum, Germany)