Master CSMI: Proposition de maquette pour 2024-2028

The EISEM report was commissioned by the Agency for mathematics in interaction with entreprises and mathematical societies(AMIES) in 2015 and updated in 2022 by CNRS INSMI to evaluate the socio-economic impact of mathematics in France. The report highlights the crucial role that mathematics plays in driving innovation and competitiveness in a wide range of industries, and identified key technologies that are central to the needs of the socio-economic world.

The CSMI Master’s program at the University of Strasbourg is specifically designed to address these needs, by providing students with advanced skills in the key technologies identified by the EISEM report. For example, the program includes courses in modeling, simulation, optimization, signal and image processing, data mining, and high-performance computing, which are all key areas highlighted in the EISEM report.

By equipping students with these advanced skills, the CSMI program aims to prepare them for careers in research and development departments of companies, service companies, specialized consulting firms, or engineering positions in universities and public or private research organizations. These are all areas where mathematics plays a crucial role in driving innovation and competitiveness, and where the skills developed in the CSMI program can make a significant contribution.

The november 2022 version is available here.

Here are some key points of the latest report:

The text highlights several areas where collaborations between the academic world of mathematics and businesses should be encouraged:

CSMI benefits greatly from its association with the local platform Cemosis at the University of Strasbourg. Cemosis plays a crucial role in fostering collaborations between mathematics, businesses, and other disciplines, creating a dynamic environment for innovation and knowledge exchange.

As a part of the regional European Digital Innovation Hubs (EDIH) network starting in Fall 2023, Cemosis will be at the forefront of accelerating the digital transformation in the Grand Est region. This network, led by Grand-Enov, aims to promote and support digital innovation across various sectors and industries. By being connected to this network, CSMI gains access to a wider ecosystem of expertise, resources, and opportunities.

The inclusion of Cemosis in the EDIH network reflects the recognition of its significant contribution to the digital landscape and its potential to drive innovation in the region. CSMI students can leverage this ecosystem to collaborate with businesses, engage in cutting-edge projects, and stay up-to-date with the latest technological advancements.

Overall, Cemosis and its involvement in the EDIH network further enhance the local and regional context of CSMI, positioning it as a program that not only prepares students with advanced mathematical and computational skills but also connects them with real-world opportunities and collaborations in the digital domain.

Starting Fall 2023, the applied mathematics team and Cemosis at UNISTRA will actively participate in two significant initiatives: PEPR Numpex and PEPR AI. These collaborations bring several benefits to CSMI students, enhancing their learning experience and future prospects.

By participating in these initiatives, CSMI students gain exposure to state-of-the-art research, collaboration opportunities with renowned institutions, and practical applications of mathematics and computational sciences. These experiences enrich their learning journey, broaden their horizons, and prepare them for successful careers in emerging and impactful domains.

The CSMI Master’s program is at the heart of the digital revolution, focusing on models, data, and algorithms. It aims to train students to be key players in the digital revolution, equipping them with cross-disciplinary skills in mathematics and computer science and a strong grasp of various application domains such as health, environment, economy, and micro-technology.

The program is designed to prepare students for the rapid technological changes and challenges in the digital world by providing them with the knowledge and skills needed in the areas of image processing, modeling, simulation, optimization, and high performance computing.

This table provides an overview of the lecture hours for each course in the first semester of the CSMI Master’s program.

This table provides an overview of the lecture hours for each course in the second semester of the CSMI Master’s program.

This table provides an overview of the lecture hours for each course in the third semester of the CSMI Master’s program.

This table provides an overview of the lecture hours for each course in the fourth semester of the CSMI Master’s program.

The name of the Master track CSMI has been used for a few years now. Changing name is not a trivial matter. We can keep the name but change its meaning. It currently means : "Calcul Scientifique et Mathématiques de l’Information".

The term "Mathematics of Information" refers to a field of study that focuses on the mathematical principles, theories, and methods used in the analysis, processing, and communication of information. It involves the application of mathematical concepts and techniques to various aspects of information processing, including data compression, coding theory, information theory, cryptography, error correction, signal processing, and more. The master track CSMI is not focused on these topics anymore and we should be careful that the name does not mislead students.

We can make the following changes:

In response to student feedback, the Master CSMI program has implemented changes to the curriculum regarding English language courses. The previous offering of two 3 ECTS English courses in Semester 1 and Semester 3, aimed at enhancing English skills, has been eliminated due to poor reception among students.

Instead, the program now includes at least 2 or 3 standard courses per semester taught in English, along with projects that require students to write reports and deliver presentations in English. This modification aims to provide students with more flexibility in their course selection while still incorporating English language instruction. By integrating English language learning within regular courses, students can develop their English skills in a more practical and contextual manner in applied mathematics and applications.

Mixing languages in a master track can offer several benefits:

However, it’s important to ensure that

Overall, a master track that combines French and English courses, along with opportunities for report writing and oral presentations in English, can offer a unique and attractive learning experience, preparing students for international collaboration and global career opportunities.

Furthermore, the Master CSMI program recognizes the potential to attract students from various European countries and beyond, taking advantage of its geographical proximity to Germany and Luxembourg. While the program previously had limited exposure to English-language courses, the curriculum changes in this document present an opportunity to appeal to a broader international student base.

By offering a combination of French and English courses, along with opportunities for report writing and oral presentations in English, the program can now cater to the needs of students from different linguistic backgrounds.

To ensure clear communication of language requirements and expectations to students:

These measures help students prepare and manage their language learning effectively.

A short survey of the current Master track CSMI teachers (13 answers) shows that 46% are willing to teach in English, 38% may be willing to do it and only 10% are not willing to teach in English. This is a good sign for the future of the program since we would like to have both courses in french and english.

The next figure show that courses may be taught in English in various ways in about the same proportion: courses taught in english completely, course taught in french but the course notes are in english, exercices in english, oral presentations and written reports can be in english. We can leverage this to implement the plan above.

In the courses section we propose a list of courses that can be taught in english. We can see that the list is quite long and that we can easily have half of the courses per semester taught in english.

The SciML courses would ideally complement and bridge the knowledge provided by the standalone Machine Learning (ML) and Scientific Computing courses in a master’s track. Here’s a brief overview of how they might fit:

In terms of the order, it would be ideal for students to first complete the ML and Scientific Computing courses, as these will provide the foundational knowledge necessary for understanding and applying SciML. The SciML courses could then be taken towards the end of the master’s track, allowing students to apply all the knowledge they’ve gained in a novel and interdisciplinary way. The final projects in the SciML courses could potentially even serve as the basis for a master’s thesis or capstone project.

Scientific Machine Learning (SciML) courses can be highly beneficial for applied mathematicians in a master’s track for several reasons:

Here is an example as of May 2023 of a SciML course:

and here is an example of introductory course for ML:

Model-driven modeling and data-driven modeling represent two different approaches to understanding and predicting system behavior. We plan on showing CSMI students how to use both approaches in their work, and how to combine them in a principled and practical way.

In the context of advanced courses at a master’s level, it can be beneficial to teach both model-driven and data-driven modeling techniques, as well as ways to combine the two approaches. This can be done in several ways:

In these advanced courses, students can be exposed to the strengths and weaknesses of each approach, and learn how to choose and apply the most appropriate modeling techniques for a given problem. They can also learn how to integrate physical knowledge with machine learning in a principled way, which is a key aspect of Scientific Machine Learning. Practical exercises and projects that involve both model-driven and data-driven modeling can be a valuable part of these courses, providing students with hands-on experience of the techniques they are learning.

Data assimilation is another powerful method that blends model-driven and data-driven modeling, and it’s often used in fields such as meteorology, oceanography, and geophysics where both model predictions and observational data are available.

There are several methods of data assimilation, including:

In the context of master-level courses, data assimilation can be a valuable topic to cover, as it provides students with practical techniques for integrating model-driven and data-driven approaches. It also provides exposure to important concepts such as uncertainty quantification and state estimation. Coursework could include practical exercises involving the implementation and application of data assimilation methods, and could cover advanced topics such as the design of optimal observation systems.

High-Performance Computing (HPC) has been an essential tool for scientific research, industry, and technology development for several decades. The scale of computational power we can harness has grown rapidly, from gigaflops in the 1990s to petaflops in the 2010s, and we are now on the brink of the exascale era.

Programs like NumPEx, the French initiative for Exascale computing, reflect this trend and underscore the importance of preparing for the next wave of computational capabilities ^[1]. NumPEx aims to design and develop the methods, algorithms and software components for future exascale machines and prepare major scientific and industrial application domains to fully exploit the capabilities of these machines.

This evolution in computing power necessitates an evolution in the skills and tools we use to harness it. The architectures of modern supercomputers are becoming more complex, with an increasing variety of hardware components that need to be programmed and optimized. The programming models we use to write parallel and distributed applications are also evolving, requiring programmers to understand and mix different programming paradigms, such as MPI, multi-threading, and GPU programming. Runtime execution systems are becoming crucial for managing the execution of programs on complex hardware.

To prepare for this future, we offer a sequence of three courses on High-Performance Computing as part of the CSMI Master’s program. These courses will give students a deep understanding of modern HPC, from the basics of parallel programming and numerical methods to the advanced techniques of hybrid computing and runtime systems. The courses will also introduce students to state-of-the-art HPC tools and frameworks, such as PETSc, that will be essential for tackling the computational challenges of the future.

These courses are not just about learning the theory of HPC; they’re about gaining practical skills that will equip students to contribute to the next wave of breakthroughs in scientific research, technology development, and industry, powered by exascale computing.

Here’s a proposed modification to the semester courses of CSMI:

In this modification, we added three courses on high-performance computing, which covers various topics such as multigrid, domain decomposition, MPI, OpenMP, CUDA, and optimization of codes for high-performance computing architectures. We also added two courses on machine learning, one on scientific machine learning. Finally, we included a course on data assimilation and digital twins in the third semester.

The following is present the courses with the skills acquired by the students in the CSMI program:

We now break down the macro skills into micro skills in the following tables

This course offers a detailed exploration of pre and post-processing techniques in scientific computation, with a particular focus on integrating these processes with network data access. It covers key topics including geometry and mesh creation, mesh modification, data visualization and analysis, and efficient use of network frameworks and APIs for streamlined data transmission.

The course underscores the practicality of incorporating network connectivity to source data from varied inputs such as sensors, images, and simulation results. It provides students with hands-on experience in managing network-based data acquisition, processing, and storage, enabling them to apply mathematical algorithms and execute data-driven pre and post-processing operations.

Designed for students in computational mathematics, data science, machine learning, and related disciplines, this course sets the stage for an introduction to High Performance Data Analysis (HPDA). It aims to empower students with the ability to leverage network functionalities for a seamless integration of data into their computational workflows.

Key benefits of the course include:

The "Network-Integrated Pre and Post Processing in Scientific Computing" course, as we discussed earlier, is designed to provide a comprehensive understanding of pre and post-processing in scientific computing, while integrating data access through networks. Looking at the course list, there are several ways this course integrates into the master track:

Overall, the proposed course can be a strong addition to the master track, providing a valuable set of skills that complements and enhances the other courses in the curriculum.

The following skills would apply to the "Network-Integrated Pre and Post Processing in Scientific Computing" course:

Here are some additional skills that could be directly associated to the course: