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Computer Simulation in Science (CSiS) is a nicely crafted inter-disciplinary program I have come across. The focussed core modules and the wide variety of application modules made it appealing. After my M.Sc. degree in Aerospace Engineering, I undertook the CSiS program to further my knowledge in Numerical methods and HPC. The intensive study program put me on the right track to face scientific questions with the right attitude and aptitude. I personally enjoyed the topics on HPC and Fire simulation. The teaching staff are well connected with the industry and research institutes, notably like Forschungszentrum Jülich, CERN, etc. In addition to the rigorous study program, students with the right motivation could get their much-needed hands on industrial and research exposure. The staff were always reachable and motivated to clarify the doubts. I was actively supported by Dr. Mohcine Chraibi and Prof. Dr. Lukas Arnold, who gave me an opportunity to work as student research assistant at the Forschungszentrum Jülich in the field of Pedestrian Dynamics and Fire simulation. This was a good learning curve with hands on scientific computing experience. I would also like to point out that Ms. Brigitte Schultz and Prof. Dr. Francesco Knechtli provided exceptional support during my study. The department also funded the language class program for the expats, to ease the integration process. The experience and knowledge gained from the CSiS program helped me secure a research associate position at the Safety Engineering Faculty, University of Wuppertal, with a focus on numerical fire simulation. The study focuses on developing methodologies for reliable fire spread modelling. With the right amount of hard work and passion, this course is a good start for a bright career in scientific computing and interdisciplinary research.
Coming from an engineering background, several aspects of the course were absolutely daunting for me at first. As a result, I found that it took me a relatively long time to fill in the gaps and understand the content, especially mathematics, completely. During this entire process, I was very thankful that all the teachers and tutors were patient and supportive and could explain concepts in larger detail if I needed it. After a period of one year like pieces of a puzzle, things started to fit in together. During my master's thesis, I was given a really good opportunity to work with Forschungszentrum Jülich with Prof. Dr. Lukas Arnold in the field of CFD performing modeling and simulation of coupled solid-fluid fire (pyrolysis) simulations. This required me to step up my game once again, requiring me to program new models which further deepened my understanding of Scientific Computing. Although the master thesis was a single person's work, I had a great team and a supporting atmosphere, especially the one-on-one time and brainstorming sessions with Dr. Arnold that not only helped me write an interesting thesis but also expanded my interests not just in CFD but to the larger field of Simulation Sciences.
Currently, I am working as a research associate in the Fluid Dynamics department at the university. My topic of research is the modeling and simulation of collisions between particles and droplets. This is a challenging task requiring me to further grow my knowledge, something that gives me a lot of joy. In general, I did find the course to be demanding, however, it was also very stimulating and eye-opening. I really enjoyed my courses in programming and mathematics of differential equations. It made me realize the potential of scientific computing in engineering, it's implications beyond the field of engineering, and most importantly, understand mathematics on a much deeper.
Already while completing my bachelor's degree studies in chemistry, I felt drawn to theoretical topics such as simulations. Thus, choosing a master's degree program which focuses on these was a natural consequence, and the CSiS program was the perfect candidate due to its four central topics: computer science, computer simulation with a focus on parallelization, numerical methods and a specialization to connect all of them. The classes and their lecturers were as diverse as the program suggests. Many lecturers have a background in physics which might grant a new way of thinking depending on one's own. Most lecturers were always willing to help, and some even offered additional courses to provide further insight into their topics. Prof. Knechtli, the head of the program, puts an immense amount of effort into improving the program and is always open to feedback.
To get the most out of the program, though, I recommend having a basic understanding of programming and mathematics beforehand; a block course at the beginning of the program will help with the latter. In my thesis supervised by Prof. Jensen, I implemented a method that calculates Stark coefficients for Renner molecules using perturbation theory, i.e., simulates the effect of electric fields on their IR spectra. After treating the field-free case relatively cheaply by applying group theory, my method approximates this effect with almost no additional cost. To this end, I combined techniques from theoretical chemistry, linear algebra, computer science and parallelization, most of which were taught throughout the program. Afterward, I decided to delve more into numerical linear algebra and have since started a doctorate in applied computer science with Prof. Frommer and Dr. Kahl. In my research, I investigate a new way to calculate matrix functions acting on vectors. It is interesting to see how often I can use the knowledge that I acquired during this program.
I joined the Computer Simulation in Science (CSiS) program at the University of Wuppertal after a Bachelor in Physics with a minor in computer science at Birzeit University in Palestine. I chose this master program because I was interested in learning experimental techniques to study physics phenomena. The CSiS program offers a mixture of mathematics, computer science and natural sciences with the focus on computer simulation to solve problems in natural sciences. During my CSiS studies, I enjoyed the lab courses the most, where I learned how to implement mathematical models such as, the Ising model, the Runge-Kutta methods and the Monte Carlo methods. I also learned how to parallelise my code and optimise it to run more efficiently. I gained knowledge from every course and practical exercise in the CSiS program, in particular, courses in data analysis, computer simulation, parallel programming and GRID computing. I also appreciated a lot the environment at the University of Wuppertal and the support of the professors and lecturers of the CSiS program. I chose the specialisation in experimental particle physics, where I carried out my master thesis in the analysis of data generated in a proton-proton collision at the Large Hadron Collider (LHC) and collected by the ATLAS detector. My master thesis was performed under the supervision of Prof. Dr. Peter Mättig and included studies on a new method to model the W-boson production in association with jets (W+jets) background process for the top-quark pair production process with the ATLAS experiment. This method models the W+jets process using Z+jets events in a data-driven approach.
After finishing my master studies, I pursued my doctoral studies with the same group and supervision as for my master thesis. The method developed during my master thesis was used and published during my doctoral work. My PhD topic is a measurement of the inclusive and fiducial top-quark pair production cross-sections in the lepton+jets channel at a centre-of-mass energy of 8 TeV with the ATLAS detector. The measurement was performed by separating the selected events into three disjoint regions and training of a neural network to improve the separation between the signal and the backgrounds. The neural network output distribution was used as a discriminant in two signal regions while the mass of the hadronically decaying top-quark was used in the third one. This configuration improved the sensitivity to systematic uncertainties affecting the measurement. A simultaneous binned maximum-likelihood fit was performed in the three regions to determine the top-quark pair production cross-section. This measurement is the most precise measurement in this channel by the ATLAS collaboration with a precision of 5.7% for the inclusive cross-section. My dissertation can be found here: http://elpub.bib.uni-wuppertal.de/servlets/DerivateServlet/Derivate-8595/dc1902.pdf
After finishing my doctoral studies, I am currently working as a postdoctoral researcher at Paderborn University in the data science group (DICE). Participating in the CSiS program paved the path for my research career and was an exceptional experience for me, I highly recommend it.
Juan Andrés Urrea
Having a background in physics and a keen interest in computational applications, the CSiS master program was the ideal next step after completing my bachelor. The compulsory courses offer a wide variety of insight in different topics related to computer simulation, computer science and numerical methods that usefully relate to the optional courses of the different specializations. The presence of good lecturers to present these topics make them more accessible and this was especially useful for me in the case of the Theoretical Particle Physics specialization, where topics taken from the first semester up to the last one were relevant for the development of my thesis, making these two years an extremely useful learning experience that I was able to fully take advantage of. An important note on this is to make sure that one has the suggested previous knowledge on the studied subjects, specially related to math, either by studying them beforehand or attending the preparatory courses also offered in the program.
At the end of the program I did my thesis in the topic of lattice QCD, under the direction of Prof. Dr. Francesco Knechtli and Dr. Tomasz Korzec, where I measured the masses of mesons composed of charm and anti-charm quark via an optimized version of the method known as Distillation, where high dimensional matrices dependent on data obtained via Monte Carlo simulations are projected onto lower dimensional subspaces to extract useful information. This work included topics of numerical linear algebra, parallel computing, statistical data analysis and particle physics, bringing together into a single project several of the concepts presented in the program. As a continuation of this I am currently doing my doctorate in the same area and continuing to apply what I learned in the master program.
After a degree in electrical engineering and several years of professional experience in computer networks, I learnt about the CSiS master’s programme in Wuppertal. That gave me the chance to reanimate my latent interests in particle physics and cosmology, hence being able to both gaining interdisciplinary knowledge and performing an appealing thesis in computer simulation in physics.
During my CSiS studies in Wuppertal, I was warmly supported by all participating lecturers and professors and the work in small groups caused an efficient increase of new knowledge. I appreciated the lab courses which contained some theory and then demonstrated numerical applications in various fields. After all, CSiS was much work but the benefit was a solid education in both computer and natural sciences.
The topic of my thesis fell into the theoretical particle physics track which, although prepared by a tutored course in lattice gauge theory, was very challenging to me. But at the end, it even lead to a publication in the journal of High Energy Physics on the Lattice in cooperation with Prof. Knechtli and other scientists from CERN and DESY.
Here’s a trial to sum up the idea of the thesis: In Lattice QCD, the space-time continuum is discretised on a 4-dimensional Euclidean hypercubic lattice. Both gauge and fermion actions are computed on the lattice and reproduce the Yang-Mills theory in the continuum limit. Some non-physical effects emerge on the lattice and need to be eliminated by numerical counterterms. Those can be won by examining symmetries; merely the according coefficients have to be determined to achieve the desired improvement. My thesis aimed at determining the improvement coefficient for the static-light axial current, being induced by a meson consisting of a light and a static quark. That happened at one-loop order perturbation theory, especially under consideration of HYP smeared actions, a technique which originally had been introduced by Prof. Knechtli.
Clearly, I had to delve into deep theory to bring together the main concepts and Prof. Knechtli was patient enough to answer my many questions, also about the basics. Besides learning the principles of lattice gauge theory, I needed to review the calculation of the involved Feynman diagrams and to understand the herein applied tools and methodologies. Based on an already existing C++ program package and with the support of the participating scientists, I could calculate and extend the Feynman diagrams to the smeared action. Finally, the improvement coefficient could be extracted as depicted in the pictures.
The final presentation about my thesis can be found here. The thesis itself is available under Theses (see left menu)
Although I did not pursue an initially intended Phd in particle physics afterwards, I was able to move into a new job within interdisciplinary research projects in the fields of informatics and physics, with a strong emphasis on software development. I found my studies in CSiS highly worthwhile as they enabled me to work in a research environment with points of contact to scientists from different fields of knowledge.
The topic of my thesis was Applying Multivariate Statistical Methods for Forecasting Electricity Price Contributors. I wrote it at Vattenfall Energy Trading GmbH (VET) in Hamburg and my Supervisors were Mr. Erik Svensson from VET and Univ. Prof. Dr. Barbara Rüdiger-Mastandrea of the University of Wuppertal.
The objective of the thesis was to develop flexible models for forecasting short and long term electricity price “contributors”, and comparing these models and the present models used at Vattenfall Energy Trading. The case studies of the electricity price “contributors” were Cross-border flows of Electricity and Margins.
Cross-border flows is the transportation of electricity between two market areas (e.g. Germany is a market area) through transmission lines linking the two different market areas. A market area is a geographical region where electricity can be transported freely, that is, without network congestion.
Coming from a mathematical background, the M.Sc. in Computer Simulation in Science with specialization in Financial Mathematics was the right programme to attend for me. It not only allowed me to make use of the Mathematical knowledge I possessed, but also allowed me to learn a lot about numerical computing and (financial) mathematical modeling concepts.
Also, I did get the tools and level of understanding required to be able to go through interviews and be selected for challenging roles. Having been working as a Forecast Analyst since graduating, I keep confirming how solid the foundations I got from the M.Sc. programme are, as well as realizing the advantage I have on the job in the combination of theory and practice I obtained from the programme.
Germán I. Ramírez Espinoza
Being a student at the master program was a great experience. I hold a B.Sc. in Engineering Physics and my interest in computing and science lead me to the CSiS master. I was looking for something more focused on the numerical analysis and the development of high performance algorithms rather than a program focused on the development of general purpose systems, like is the case in some IT master courses.
I had the opportunity to get taught by great professors from a wide range of areas of science: from physics to computer science to mathematics. This surely gives the student a better approach to the topics taught, the possibilities of research, and the connection between areas of science that, at first sight, seem disparate, like economics and physics.
After the completion of the master I was offered a job at EON, an energy company which also engages in trading for hedging purposes, in the area of risk management as developer of mathematical algorithms to support decision making and risk compliance.
The computational representation of partial differential equations (PDE) can be challenging in some cases and special numerical algorithms must be created to achieve reliable results. My thesis deals with the convection-dominated behavior present in the computational simulation of convection-diffusion PDEs. This behavior is caused by the parameters of the PDE and lead to incorrect approximations of the function of interest. Moreover, the derivatives of this approximation are even worst. In financial mathematics, the derivatives of the price of the option are required to measure the sensibility of the price to different parameters like the volatility.
In computational finance, there exist various methods for the pricing of Options, and one of them is the numerical simulation of the celebrated model called the Black-Scholes equation. This model is a convection-diffusion PDE and in many cases the parameters are such that convection-dominated behavior is present.
Three methods are presented and emphasis is put on the Kurganov-Tadmor (KT) scheme. The KT scheme delivers excellent results and handles discontinuities or non-smoothness on the initial condition satisfactorily. In comparison to other methods like Crank-Nicolson or F inite Volume Methods, the KT scheme performs competitively and, additionally, it is easy to implement.
In the image, the approximation to the first derivative of price of the option is shown. Unrealistic oscillations artificially introduced by the method appear.
In many cases, Monte Carlo methods are used because of the ease of implementation and flexibility. Nevertheless, when the dimensionality of the problem is not high, using an scheme like the KT represents advantages and a considerable optimization in terms of computing time. This method could help the financial analyst to obtain approximations to the price of an option and its derivatives in an accurately manner.
CSiS program at Bergische Universität Wuppertal was a great experience to me, even though I did not finish the master program. I cannot say what I value more, the multicultural experience of living in Germany alongside people from all over the world, or the master program itself. I really appreciated the lectures that I had, they gave me a new overview about the world and, if I had the appropriate age, I would go for it again. On the other hand, a new career opportunity appeared in another country (Canada) as a consequence of my hobby (programming) and the Computer Science module studied here, and, as I already had a master of science degree in another field, I decided not to waste it and leave the CSiS program.
One important piece of advice that I would give to anyone coming here is to make sure they study the German language as well.
Overall, I thank everyone that helped me get here and do my studies, it was a great experience and a great opportunity.
CSiS program is an excellent interdisciplinary master course, which combines science theory with modern computational technology and can build strong theoretic background in the future study in simulations. During the course, I was enjoying the concept world of physics, math and programming. This promotes the capability of reasoning, construction and logic thinking, which is a great help for the students, who wants to work in the area of informatization in the manufacturing industry.
The topic of my thesis is Validation of Atmospheric Infrared Sounder Temperature Retrieval. It is about the intercomparison of the temperature mean and RMS value between three different data source for four different atmospheric conditions, the work was carried out in research centre Jülich, and was supervised by an expert in remote sensing, Prof. Martin Riese, as well as Dr. Lars Hoffmann.
In the plot is the Temperature RMS comparison for the midlatitude, which shows good consistency in the results of other previous published articles.
After a diploma in pure mathematics I detected the master degree course Computer Simulation in Science I decided to take part in this study because I wanted to change my focus to an interdisciplinary subject, and this course is a mixture between mathematics, physics and computer science with focus on the computer simulation.
I gained good experience with it: There were only a few students in the class and very kind and helpful lecturers.
During the studies, I liked the compulsory subject Computer Simulation at most, especially the simulation of physical systems. Before, I had no experience with physics and learned a lot thanks to patient lecturers and much work.
Moreover, for me it is impressing that the compulsory subjects enable you to choose one of the quite different elective subjects. For example, I visited lectures in mathematical modelling, theoretical particle and atmospheric physics.
At the end, I wrote an multdisciplinary thesis including numerical mathematics and theoretical particle physics in the subject Mathematical Modelling. This work was very good supervised by a mathematician, Prof. Dr. Michael Günther, as well as a physicist, the CSiS chairman Prof. Dr. Francesco Knechtli.
The title of my master thesis is Implicit partitioned Runge-Kutta integrators for simulations of gauge theories and can be described as follows:
In the simulations of gauge theories, expectation values of certain operators have to be calculated. This is usually performed using a Hybrid Monte Carlo (HMC) method that combines a Metropolis step with a Molecular Dynamics step. During the Molecular Dynamics step, Hamiltonian equations of motion have to be solved through an integration scheme.
Thereby, the integrator has to fulfill the properties time-reversibility and area-preservation. There are state-of-the-art integration methods with these properties, e. g. the Leapfrog scheme as well as splitting methods. At the beginning of this thesis, there was the question if there are any higher order numerical integration schemes for simulations of gauge theories besides the aforementioned methods.
I investigated implicit Runge-Kutta schemes on Lie groups. First of all, I have rewritten the Leapfrog scheme as Runge-Kutta scheme of second order. Afterwards, I focused on higher-order Runge-Kutta methods and developed a time-reversible scheme of order 3. Finally, I implemented a code and performed a HMC simulation using the different integrators.
In the image, the convergence order of the different integration methods can be observed.
After the studies, I started to work in the University of Wuppertal. I have been an employee in the atmospheric physics sector for 1.5 years and changed to the applied mathematics / numerical analysis. At the moment, I write a PhD thesis that proceeds with the work done in the master thesis.
Konstantinos A. Sofos
A question that anyone could have when applying for a master degree, particularly in a different country, is likely to be, “What am I going to get out of this?” It is difficult to foresee your future and estimate the long-term outcome of your decisions. For this reason, it is rewarding to see that your efforts came through and thank people who helped you on your way.
As aptly put forth by Sir Isaac Newton: “If I have seen further it is by standing on the shoulders of giants”. The academic guidance and support I received as part of the CSiS program was exemplary.Coming from a Physics background, I felt very excited about the opportunity that by attending this program I would be able to gain a deep understanding of various mathematical methods and their applications in Finance. Here, I gained expertise in simulation and optimization techniques, stochastic calculus, financial mathematics, statistical data analysis and discrete mathematics.
The topic of my thesis was “Numerical Pricing and Risk Management of Energy Commodities Derivatives” and the aim was to study pricing and hedging strategies of energy derivatives (Options, forwards, futures) using single and multi-factor pricing models. A good understanding of the stochastic price dynamics was required for these purposes.
In parallel to my studies, I was working at E.ON Global Commodities SE as a working student. This naturally drew me towards a career in the energy industry and a European dominant E.ON SE.