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Student workshop on Applied Mathematics (SWAM)

Date: 17/11/2022 09:00 - 19/11/2022 14:00
Place: Sokolovská 49/83 & Malostranské nám. 2/25

 
The Student workshop on applied mathematics is organized with the help of the 4EU+ Alliance. A limited number of students from Heidelberg University and the University of Copenhagen will be funded by the 4EU+ Alliance. The workshop is intended primarily for master's and doctoral students. The purpose of this workshop is to bring graduate students studying applied mathematics in natural sciences, engineering, and mathematics together and create an environment to share ideas from different perspectives and to enable easier communication with researchers for possible interdisciplinary international collaboration.

Students that are not registered for the workshop are also welcome to join lectures (or just one particular lecture) given by invited speakers from various fields including applied mathematics, natural sciences, computer science and engineering, as well as presentations of international PhD students (see the programme and conference booklet below). 
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From the Press

Article published before the worshop here (Czech only).
Article published after the worshop here (English).
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For registered participants, the workshop will include a student meet-up on Wednesday, a workshop dinner on Friday and a city tour on Saturday evening. A more detailed program will be published on this page in November. In addition to lectures by invited professors (see below), students will have the opportunity to present their work in a short presentation with a minimum duration of 15 minutes and maximum of 30 minutes including discussion. The deadline for short talk and registration submission is October 17, 2022. There is no conference fee, but the number of participants is limited.

We ask participants who are interested in presenting their work at the workshop to send the abstract of their lecture to the e-mail studentworkshop@4euplus.eu by October 17, 2022. The abstract should be sent in PDF format and follow the instructions in the template, see below in the attachment.

If you have any questions about the conference or face any problems (e.g. using the abstract template), please contact us via e-mail.

Contact e-mail: studentworkshop@4euplus.eu
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Practical information

Accommodation: Accommodation for students funded by 4EU+ Alliance is provided by Hotel Adeba (in twin rooms including breakfasts). Hotel Adeba is located 600 m from Campus Karlín. We kindly ask other students who are interested in booking a room in the same hotel to write an e-mail reservation@adeba.cz (ideally) by 21 October using the keyword SWAM. The price for our group is 1090CZK/night/single room (including all taxes, Wi-Fi and breakfast). Of course, you can find other hotels nearby via lodging websites like booking.com or airbnb.com. 

Transportation: Travelling by city transport is only possible with a valid ticket. Passengers have to obtain their tickets before boarding the vehicle or entering the subway system (in buses, the tickets can also be purchased by the driver). There are the same tickets for trams, buses and subway. The price for a 30-min ticket is 30CZK and for a 3-day ticket 330CZK, see here.
The tickets can be purchased at all subway stations, selected newsstands, travel bureau or by mobile phone application "Lítačka" (Apple or Android).

A connection search can be found on the official website of DPP here, and a general guide on how to use the tickets here.

Conference venue from the airport: Campus Karlín is located very close to the Křižíkova subway station (subway line B - the ''yellow'' one). The quickest way of getting from the Ruzyně airport to Křižíkova is by taking bus number 119 from the Terminal to station Nádraží Veleslavín (subway line A - the ''green'' one). From there take subway line A to transfer station Můstek, transfer to line B, and continue by subway to station Křižíkova. Křižíkova is also on the tram line of lines 3, 8, 24.
Malá Strana Campus is located at Malostranské náměstí. The closest tram stop is right in front of the building (lines 12, 15, 20, 22, 23). Not far from the campus, about 10 minute walk, is the metro station Malostranská (line A).

Covid restrictions: There are currently no covid restrictions for arrival to the Czech Republic. Respirators and medical masks are mandatory only in hospitals and pharmacies. 

Time zone: In November, the time zone is UCT+1:00, see here.

Currency: The currency in the Czech Republic is the Czech Crown (CZK). An approximate exchange rate is 1 EUR = 25 CZK.

National holiday: 17 November is a national holiday in the Czech Republic (International Student Day and Struggle for Freedom and Democracy Day). The opening hours of small shops or restaurants may differ. 

Electricity: For Czech Republic there are two associated plug types, types C and E. Plug type C is the plug which has two round pins and plug type E is the plug which has two round pins and a hole for the socket’s male earthing pin. The Czech Republic operates on a 230V supply voltage and 50Hz.

Restaurants: Lunch is not funded by Charles University. There are lots of options where to go for lunch/dinner near the faculty building, such as Vegetarian/Vegan – Dhaba Beas, soup – Polévkárna, Vietnamese - Banh—mi—ba, Czech – Lokál, and pizza – 360 pizza. Be aware that the opening hours can change due to the national holiday.

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List of invited lecturers (will be updated):

Jakob Zech (Heidelberg University)
Melina Freitag (University of Potsdam)
Rolf Poulsen (University of Copenhagen)
Cristóbal Bertoglio (University of Groningen)
Martin Stoll (Chemnitz University of Technology)
Jens Saak (Max Planck Institute for Dynamics of Complex Technical Systems)
Jan Papež (Czech Academy of Sciences)
Roman Neruda (Czech Academy of Sciences)
Petr Minařík, Ondřej Hroch (Keen Software House)
Oldřich Semerák (Charles University)
Friedemann Kemm (BTU Cottbus-Senftenberg)

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Jakob Zech – Large Scale Bayesian Inversion: Sparse-Grid and Transport Methods

Abstract:
Bayesian inference provides a rigorous framework to learn unknown parameters from noisy data. As such it has become a ubiquitous tool in modern machine learning and applied mathematics. From a practical perspective, it requires the approximation of high-dimensional integrals. Common approaches to do so include (i) sampling methods and (ii) specifically devised deterministic quadrature rules. In this talk I will discuss transport based sampling and sparse-grid quadrature as two instances of such algorithms. Additional to explaining how they can be used to perform parameter inference, I will give some insight into why these methods can deal with high dimensionality for certain PDE driven inverse problems.

Rolf Poulsen – Tools for Modern Computational Finance

Abstract:
Under very general conditions – but for surprisingly subtle reasons – a key part finding a sensible price for any financial contract is the calculation of expected values. After briefly reviewing the arbitrage-free pricing of a call option in the Black-Scholes model, I describe some tools used in modern computational finance. More specifically, but deliberately teasingly, this will involve some of the following concepts and names:
  - Scripting languages and smart contracts.
  - Fourier inversion and the return of complex analysis
  - Sobol, Longstaff-Schwartx, Craig-Sneyd
  - Automatic adjoint differentiation
  - Differential machine learning

Martin Stoll – From PDEs to data science: an adventure with the graph Laplacian

Abstract:
In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples.

Melina Freitag – From Models to Data and Back - An Introduction to Data Assimilation Algorithms

Abstract:
Data assimilation is a method that combines observations (e.g. real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system. The model is usually represented by discretised time dependent partial differential equations. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we derive the most important variational and sequential data assimilation approaches, in particular three-dimensional and four-dimensional variational data assimilation (3D-Var and 4D-Var), and the Kalman filter. The final part reviews advances and challenges for data assimilation.

Cristóbal Bertoglio – Inverse problems in blood flow modeling

Abstract:
Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. In this talk I will present some of the inverse problems in blood flows formulated in our group, in particular from data coming from Magnetic Resonance Imaging and including fluid-structure interaction models.

Jens Saak – A journey to digital twins of machine tools

Abstract:
Industry 4.0 requires the design and control of complex models, which generally need to be fitted to measurement data and made suitable for real-time control applications; e.g., digital twins and digital shadows serve as computer-based representations of machines and processes during the entire product cycle. In this talk, we will evaluate strategies for modeling and model order reduction of machine tools, i.e. machines that are used to build (parts of) machines. Thermo-mechanical models for the machine tools feature a couple of challenges for both modeling and order reduction techniques:
  - To limit the effort, usually stationary elasticity is coupled with transient heat equations, rendering the full model a differential algebraic equation.
  - While the heat distribution and elastic deformation can be modeled by linear partial differential equations, some components like bearings and guide shoes feature nonlinearities that are crucial for correct representation of the machine behavior.
  - Modern machine tools feature up to 6 axes along which parts can be moved for optimal placement of the tool relative to the work-piece. On each of these axes, two parts of the machine are moving relative to each other making the entire model time-varying. Over the recent decade, we have worked out methods to address all these challenges and created an automated workflow for practitioners using both proprietary and open-source tools to create and use the desired digital representation for each task.

Jan Papež - Can a computed result be relied on?

Abstract:
Real-world applications often give rise to complex and challenging problems that can only be solved numerically. In order to reduce the complexity of the problem and allow us to get an approximation within the given time using available computational resources, one has to consider some simplifications, which typically introduce various errors. We should then ask how accurate is the computed approximation and whether it can be used for the original application. This can be answered by so-called a posteriori error estimates that are based on the properties of the problem to be solved and evaluated from the computed approximation. In the talk, we will present some error estimates for numerical solution of partial differential equations.
Roman Neruda – Adversarial examples: how safe are machine learning models

Abstract:
Adversarial examples are special inputs to machine learning models intentionally designed to cause the model to make a mistake. They represent an important issue concerning security and generalization capabilities of models deployed in practical applications. In the talk we will present several approaches of adversarial attacks for image classifiers, and sketch possible defense strategies.

Petr Minařík – Realtime Interactive Volumetric Water Simulation

Abstract:
Water, water everywhere. This talk will focus on illustrating a modern approach to water simulation in video games. This novel solution provides realistic simulation, during real time play, and as a mechanic of play. We will share working examples of our solution, including an algorithm that illustrates our core concepts.

Oldřich Semerák – On the marmoreally beautiful and yet unlovely sides of Einstein equations

Abstract:
On January 24, 1938, Albert Einstein wrote to Cornelius Lanczos: “I began with a skeptical empiricism more or less like that of Mach. But the problem of gravitation converted me into a believing rationalist, that is, into someone who searches for the only reliable source of Truth in mathematical simplicity.” Mathematics (Riemann-type geometry) played a fundamental role in Einstein’s quest for the new theory of gravitation. We will shortly recall when and how geometry entered the game, why the left-hand (“geometrical”) side of the Einstein equations is so elegant, and why their right-hand (“physical”) side likely has to remain unlovely.

Friedemann Kemm – How to prepare a scientific presentation
 
Abstract:
This will be a talk about talks. Giving a presentation in mathematics or science in general shares some issues with presenting science in written form and with giving a public speech in general. Especially the latter is often forgotten when it comes to presenting on a conference in science and mathematics. We will discuss some general strategies how to convey a message in a public talk and some techniques in preparing slides for a presentation that will be helpful in this context.


Workshop poster  ABSTRACT_TEMPLATE  Conference booklet  Workshop schedule  group_photo  group_photo_small