ECMI Modelling Week 2023

Szeged, 09–16 July, 2023

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Bolyai Institute University of Szeged

The 36th ECMI Modelling Week will take place on 09–16 July, 2023
at the University of Szeged, Hungary.

ECMI has been running annual Modelling Weeks for students since 1998. Students come from all over Europe to spend a week working in small groups on projects which are based on real-life problems. Each group is led by an ECMI instructor who introduces the problem – usually formulated in non-mathematical terms – on the first day, and then helps to guide the students to a solution during the week. The students present their results to the other groups on the last day and then write up their work as a report.

The main aims of the Modelling Weeks are: train students in Mathematical Modelling and stimulate their collaboration and communication skills, in an international environment.

Attendance at a Modelling Week is an integral part of the ECMI Certificate and of many of the masters courses run at ECMI centres, but many other students have also learned new skills by attending one of these very successful courses.

A number of similar Modelling Weeks or Modelling Camps are organized by ECMI members each year. 2023 at the University of Szeged, Hungary.
A full list of previous events can be found here.

Problems and instructors

Special functions in modelling of optical vortex propagation

Ireneusz Augustyniak (Wroclaw University of Science and Technology, Poland)

The topic is related to off-axis vortex beam propagation through the classical optical system. In the microscope, the Gaussian beam with embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. The task is to calculate Fresnel integrals and present an analytical model of the optical vortex scanning microscope.

The main goal is analytical solutions using special functions.

Keywords: integral, special function, optical vortex.

Application of data-driven models in hydrological forecasting

Zsolt Vizi (University of Szeged) and Péter Kozák (Water Management Directorate of Alsó-Tisza, Hungary)

The precise prediction of water levels of rivers is crucial for societies, as it supports the mitigation of flood hazards, the planning and management of water withdrawal, and drought prevention. In Central Europe, Hungary, the water level of rivers has been recorded since the early 19th century, and various water level and flood prediction methods were developed during the centuries. Since data recording was significantly improved in the last 30 years, there are large and just partially used datasets in the water management domain. The project involves understanding the time series data collected at various gauging stations and applying data-driven methods either to extract patterns from the data or to predict water level for multiple days ahead from a multivariate time series data.

The main goal is to set up a minimal framework including processing pipelines and providing insights about potential usage of data in the water level forecasting.

Keyword/skills: Python programming, data-driven methods, time series, networks, independence analysis

Determinants of COVID-19 Pandemic Outcomes In Canada: A Retrospective Data-Driven Analysis

Seyed Moghadas (York University and Agent-Based Modelling Laboratory, Canada)

We will utilize a fairly comprehensive data set for pandemic outcomes in Canada, including confirmed cases, hospitalization, intensive case unit (ICU) admission, and death, stratified by age, gender, and time of event to understand the temporal variation in the outcomes. Statistical and regression analysis will be conducted to determine the differences in risk of outcomes in different age groups, and in pandemic waves. This will be a descriptive analysis that can shed lights on the burden of pandemic and the effect of interventions.

The main goal is to provide an understanding of variations in the burden of COVID-19 pandemic over time.

Keywords/skills: regression, data analysis, model fitting, effective communication

Is Country X adequately prepared for an influenza pandemic?

Beatrix Oroszi (National Laboratory for Health Security, Hungary)

Influenza A(H5N1) epidemics are common in certain animals and the virus occasionally infects humans. If the virus could easily spread from human to human due to changes in its genetic makeup, it would have pandemic potential. A simple deterministic mathematical model could provide a new basis for pandemic planning and preparedness.

The main goal is to use a mathematical model for scenario analysis and provide evidence-based answers to crucial questions for decision-makers (e.g. on vaccination targeting, and non-pharmacological measures).

Keywords/skills: deterministic model, scenario analysis, input parameters, vaccination programs, evidence-informed decision making

Entropy based estimation of remaining useful life in ball bearings.

Landauskas Mantas (Kaunas University of Technology)

Rotational machinery is heavily dependant on ball, roller or other types of bearings. Bearings often have an estimated lifespan of about 10 years or hundreds of millions of revolutions under normal operating conditions. But actual operating environment may be rather demanding and fall well out of the definition of normal. Machinery in mining industry experiences maximum loading conditions and breaks are costly, aviation must comply with strict safety measures just to name a few. Thus estimation of remaining useful life of bearings is important in many aspects.

Classical approach on estimating the remaining useful life of a bearing would be statistical or frequency analysis of the corresponding vibrational data. Although state of the art techniques mostly uses entropy based feature extraction. Different types of entropy itself or permutation entropy are investigated, various multiscale and hybrid approaches exist. Even so for fault classification problems.

Permutations or ordered patterns coupled with entropy have two main advantages as feature extraction techniques compared to statistical approaches: they enable to capture nonlinear patterns in data and provides certain degree of robustness to noise. Permutation entropy based feature extraction will be the main line of the project. The features then would be passed to appropriate machine learning method to predict the remaining useful life of a bearing. Ordered patterns could be sampled from the vibrational data in various ways including temporal, multiscale or even indirect spatial approaches. This creates a wide pool of mathematical exploration ideas for the week.

The recommended data set for the project would be widely known NASA bearing data set. It comprises of several run to failure experiments. There are other alternatives also. Lots of numerical experiments will need to be performed and Python is recommended as programming language.

The main goal is to develop permutation entropy based feature extraction technique for vibrational data to predict remaining useful life of a ball bearing.

Keywords/skills: ordered pattern, entropy, remaining useful life, machine learning.

Quantum modelling and numerical simulation of an atom driven by a strong laser pulse.

Attila Czirják and Attila Tóth (ELI-ALPS)

A suitable short laser pulse with sufficiently high peak intensity (in the 100 TW/cm^2 range) is able to excite the atoms of a dilute noble gas sample such that they emit an XUV "light"-flash with temporal pulse length in the 100 attosecond range, enabling the corresponding temporal resolution of certain measurements, which revolutionized the past 2 decades of atomic and molecular physics. At the hart of this is a single atom's response to the laser pulse, which can be numerically simulated by solving the corresponding Schrödinger equation. However, a weak response has to be computed very accurately, which challenges traditional methods and algorithms.

The main goal is to develop and test a simulation code based on a novel numerical approach.

Keywords/skills: attosecond physics, numerical solution of partial differential equations, programming with focus on numerical accuracy and performance

Stereo depth camera calibration and controll support system.

Szabolcs Szalánczi and Péter Zalka (B+N Referencia Zrt.)

In the field of robotics, tracking the position of a device is a common problem. Usually the build in solutions are not as accurate as the developers would like or the synchronization of different sensors are too difficult. One part of the problem is to project the depth data to a predefined plane and to reduce the measurement error of the sensor. Optionally the built in IMU (inertial measurement unit) can be used to track the movement of the device in addition to image processing. The sensor for this project is the Intel RealSense Depth Camera D435i, which we can use with the pyrealsense2 module.

The main goal is to create a framework to handle and correct real-time projection of BGR and depth camera data. Optionally the framework can be expanded the built in IMU data.

Keywords/skills: computer vision, projective geometry, statistics, python programming.

Insurance premium calculation.

Dora Selesi (Faculty of Sciences, University of Novi Sad, Serbia)

In actuarial mathematics, one of the main goals is to provide appropriate models for fair premiums to be calculated by means of various statistical methods. Non-life insurance lines such as car insurance, or proprietary insurance are more challenging due to the underlying uncertainty types. Claim sizes and number of claims are separately modeled by statistical distributions and data-fitting methods. Aggregate claim sizes for a portfolio of insurance policies can be obtained by probabilistic methods for summing i.i.d. random variables. These methods provide the so-called manual premium for a larger population. More advanced models require an in-depth analysis of risk parameters based on risk classes stratified by gender, geographic region or other possible predictors, as well as Bayesian credibility factors assigned to the empirical claim size data.

The main goal is to calculate the fair premium for a portfolio of insurance policies based on data of previous claim sizes and previous number of claims for a certain non-life insurance line of business.

Keywords/skills: probability, statistics, financial and actuarial mathematics.

Inverse methods in freeform optical design

Martijn Anthonissen (Eindhoven University of Technology)

When it gets dark and we switch on the lights, we want to be surrounded by comfortable light. The light source is typically an LED that is combined with reflectors and lenses to send the light where you want it to be. Given the light distribution of the source and the desired target distribution, what is the optical system (reflector, lens or combination thereof) that does the job? That is the question we need to answer! This field is freeform design and it is used for, e.g., car lights, luminaires and street lights.

To find the optical components there are two approaches: direct and inverse methods. In direct methods an optical component is designed in a CAD tool and the light distribution is calculated using ray tracing. We follow many rays from the source to the target using the laws of optics (Snell’s law, law of reflection). If the obtained light distribution deviates from the desired one, the CAD geometry is adjusted, and a new light distribution is calculated. This is typically a slow process and it needs an experienced optical designer.

Alternatively, the problem is solved as an inverse problem. In inverse methods the shape of the lens or reflector is calculated directly by solving an appropriate partial differential equation (PDE), avoiding iterations and manual optimization. This nonlinear PDE is of Monge-Ampère type.

An example about a 2D reflector system that converts a point light source with a Gaussian energy distribution into a parallel light beam with a uniform distribution can be seen here.

The main goal is to compute the optical system that converts a given light source into a desired target distribution. This is done by solving differential equations numerically.

Keywords/skills: Numerical solution of differential equations, freeform optics, geometrical optics, Matlab or Python programming

Computer-Based Numerical Experiments of Cell Populations

Peter Boldog (Wigner Research Centre for Physics, Bolyai Institute, Hungary)

With the rise of personalized therapeutic approaches, computational drug testing, and artificial tissue engineering, modeling cell cultures has become a prominent field in mathematical and in silico biology. To be successful in these areas, it is crucial to understand the complex collective behavior that emerges from simple phenomena such as migration, proliferation, and intercellular communication.

Cells are mesoscopic discrete entities within a multicellular organism, existing on a scale much larger than the molecules they are composed of, yet much smaller than the organism itself. When it comes to mathematical models describing cells, our typical expectations are that they should be capable of describing a large range of cell numbers, including extremely low counts, account for spatial distribution, and enable the investigation of various phenotypes.

In this project, students will utilize agent-based stochastic simulations (ABM) to study the response of cell cultures to drug treatments. Unlike continuum models, ABMs treat each particle as an individual that follows a prescribed set of rules. By analyzing the collective behavior of these agents using statistical methods, information about the system can be obtained. This technique provides a comprehensive description of individual behavior and considers stochastic effects arising from the finite number of agents and their interactions.

The main goal is to develop a stochastic simulation framework that can depict the time evolution of cell cultures, run simulations, and investigate the effects of drug dosage.

Keywords/skills: agent-based methods, stochastic simulation, scenario analysis, cell population, Python programming


The groups have to submit a report to the organizers after the event, use a template for this document here.

The deadline for the FIRST submission is 1. August, 2023. This document has to be sent to the instructor and the organizers, the instructor can give feedback and comments for revision.

The deadline for the FINAL submission is 30. August, 2023. This is the final version of the document containing all modifications requested by the instructor.


Program table



The conference will be held in the Bolyai Building of the University of Szeged in Szeged, 170 km south-east from Budapest. It will be organized by the University of Szeged, Bolyai Institute (Aradi vértanúk tere 1.).

With 2,100 hours of sunshine each year, Szeged is called "the city of sunshine". It is the most important city on the South Great Plain and the economic, scientific and cultural centre of the region. The proximity of the three borders provides Szeged a significant strategic role both for Europe and for Hungary.

Szeged is located less than 20 km from the Romanian and Serbian borders, at the confluence of two rivers: the Maros and the Tisza. It is 170 km far from Budapest and 220 km far from Belgrade. Its population numbers more than 162,000, making Szeged the second largest provincial city in the country.

From December 21, 2007 Hungary is a member of the Schengen Area, and applies the Schengen legislation in full. For details on visa rules and visa waiver agreements please check the website of the Ministry of Foreign Affairs.

All participants will be accomodated in the prestigious Art Hotel , just a couple of minutes walk from the Bolyai Institute.


1. Szegedi Nemzetközi Néptáncfesztivál - International Folk Dance Festival in Szeged

13 July
  • 17:30: parade from Széchenyi Square through Kárász Street to Dugonics Square.
  • 18:00: opening ceremony (Short folk dance performances by 3 Hungarian and 4 Foreign dance groups.) on Dugonics Square.
  • 20:00: folk evening in the Kisszínház. You can request free tickets here: IH Rendezvényközpont (IH Events Centre)
  • 14 July Performances by foreign dance companies in cultural centres.
  • 17:30: Slovak dance group, place: Heller Ödön Művelődési Ház
  • 18:00: Albanian dance group, place: Kecskési Művelődési Ház
  • 18:00: Turkish dance group, place: Petőfi-telepi Művelődési Ház
  • 18:00: Serbian dance group, place: Tömörkény István Művelődési Ház
  • All performances are free, but you must register for the Serbian dance group, by sending an email to
  • 15 July
  • 19:00 Gala performance at the Nagyszínház. You can request free tickets here: IH Rendezvényközpont (IH Events Centre)

  • 2. LÖSZ Kulturális Fesztivál - LÖSZ Cultural Festival in Hódmezővásárhely (Szürkekabát Bárszínház) 14-15 July

    Hungarian traditional event. Folk dancers, folk music, fair, children's activities, horse riders and bogrács (Hungarian goulash soup), folk music and rock concerts. It is 55 minutes by public transport and 30 minutes by car from the centre of Szeged. It is easily accessible from Széchenyi Square/Aradi Square by TramTrain. An ABC zone ticket is required for travel, which costs 465 HUF and can be purchased from a ticket machine at Széchenyi Square or Aradi Square.

    3. Events in Móra Ferenc Park, Szeged

    • 8 July 15:00-19:00 - Szeged Military Orchestra Festival
    • 9 July 19:00 - Performances by Czech, Slovak and Estonian folk dance groups
    • 15 July 19:00 - Performance by brass band and majorette group
    • 16 July 19:00 - Performances by Portuguese and Slovak folk dance groups


    Sights of Szeged


    Useful informations: Download

    How to reach Szeged

    By plane

    The International Airport of Budapest is located 160 kms from Szeged. From Budapest Airport you may continue your trip to Szeged by train (please see it below).

    By train

    Trains depart at hh:53 every hour between 5:53 and 20:53 from Budapest "Nyugati pályaudvar", on the backward direction the departure time is usually hh:45 every hour between 4:36 and 19:45 from Szeged. You are recommended to check the schedules for this destination, because the start times and changing points might vary due to some railway reconstruction works. On the same page you can check the prices and schedules of other destinations as well.

    How to get to Szeged from Budapest Airport by train?

    There is a train station close to the airport. After arrival, you need to take the bus 200E (leaves every 7-8 minutes from the airport during daytime) to the train station. You have to get off at the bus stop "Ferihegy vasútállomás". The ticket can be purchased from the ticket vending machines at the bus stop of the airport or on the bus as well. The bus leaves from somewhere in the middle, between Terminals 2A and 2B (they are very close to each other).

    After getting off the bus, you have to cross the road through the pedestrian bridge. There are two railway tracks, you have to go to the one which is further from the road. Go to the very end of the pedestrian bridge and go down the stairs. When you arrive at "Ferihegy" train station, you can buy a train ticket from the ticket vending machine or in the phone application named MÁV. You can also buy your ticket online here.

    You need to buy train ticket to Szeged, the prices and the timetable can be found here. Trains leave from Ferihegy train station to Szeged hourly always at hh:13 minutes, and the travel takes two hours. It is recommended to buy also an InterCity ticket for an extra fee, for which you will get a fixed seat in a better compartment. The InterCity tickets for seat reseravtion contain the number of the carriage (kocsi in Hungarian) and the number of the seat (hely in Hungarian). Please look for these carriages at the very end of the train. Szeged is the terminal station of the train, so you do not need to check where to get off.

    From the railway station you can easily reach the Bolyai Building by tram or a twelve-minute-long walk (about 1 km). Take the tram No. 1 or No. 2 in front of the railway station and get off at the 3rd stop (Aradi vértanúk tere).

    Tickets for buses and trams can be purchased in kiosks, from ticket vending machines (430 HUF), can be bought from the drivers or from the ticket vending machines on the bus/tram (600 HUF or 500 HUF). A weekly ticket costs 3300 HUF. In particular, you can purchase bus tickets inside the building of the railway station, downstairs at the exit. Timetables and maps of local transportation can be found here.

    By GreenShuttle

    A more expensive, but really comfortable direct shuttle is available for 11400 HUF by the company Greenshuttle. Their cars take you from Budapest airport to your hotel door in Szeged. The maximum waiting time at the airport is 30 minutes for a "green" shuttle, while the more economic "orange" transfer operates with a 2-hour maximum waiting time for 8800 HUF. It is recommended to book the shuttle 48 hours before departure time, otherwise a 20% extra charge is applied. For more info: check this page.

    By bus

    Direct bus lines are available from/to many cities. You might check the bus schedules.

    Parking and public transport in Szeged

    There are many parking places in the downtown near Aradi vértanúk Square. Szeged has a prepaid ticket parking system: inside the middle boulevard and in some other places you must have a prepaid ticket under your windscreen on weekdays (mostly between 8:00 and 18:00 but check the signs), and for some places on Saturday too. You can buy the ticket from the ticket machines where you can pay by credit card or in cash, but tickets may also be bought by SMS, telephone or a mobile application.



    • Csilla Kertész (

    Scientific Committee:

    • Gergely Röst (
    • Attila Dénes (
    • Nóra Juhász (
    • Zsolt Vizi (