Modeling Seminar

Description

This course proposes modelling problems. The problems can be industrial or academic. Students are faced to an industrial problem or an academic problem (research oriented). They are in charge of this project. An teacher/tutor may guide them to find solutions to the problem. For industrial project, they have to understand the user needs, to analyze and model the problem, to derive specifications, to implement a solution and to develop the communication and the presentation of the proposed solution. More academic projects are linked to the courses. They are constructed such that the students can go deeper into a subject.

2024-25 subjects

Subject: Modelling and High-Performance Computing for the Gordon Bell Awards

Supercomputers play a crucial role in simulating complex phenomena of our real world, ranging from climate modeling and molecular dynamics to astrophysics and material science. These simulations help scientists understand systems that are otherwise too large, too small, or too complex to observe directly. However, the ability to accurately simulate these phenomena depends not only on the physical models but also on how these models are translated into a form that computers can process efficiently. This requires transforming the continuous mathematical models of real-world systems into discrete forms suitable for computation—a process known as discretization. But even with accurate models, ensuring that they can run efficiently on supercomputers, which feature cutting-edge hardware architectures, presents a significant challenge. Therefore, both the modeling and the discretization processes must be carefully designed to fully exploit the power of modern supercomputing resources.

Clearly, a multi-level design approach is necessary to bridge the gap between the abstract models of physical systems and their practical simulation on high-performance computing (HPC) platforms. This involves considerations at several levels, including algorithm design, software optimization, and hardware-specific tuning, in order to achieve the best possible performance. Factors such as parallelism, memory hierarchy, communication overhead, and load balancing must be carefully addressed to ensure the simulation scales well as the size of the problem and the number of processing elements increase. The goal is to make full use of the massive computational capabilities of supercomputers, often composed of thousands to millions of cores, while minimizing inefficiencies.

As part of this seminar, you will investigate recent papers from the Gordon Bell Award winners, which is one of the most prestigious honors in the field of high-performance computing (HPC). This award, often referred to as the “Nobel Prize of supercomputing,” recognizes the most groundbreaking and high-performing simulations executed on the world’s fastest supercomputers. By studying these award-winning papers, you will gain insights into the state-of-the-art techniques employed in various scientific domains to achieve record-breaking computational performance. You will explore the advanced models used in these simulations, as well as the numerous technical challenges and optimizations required to ensure efficient execution on supercomputers. This includes understanding the mathematical modeling process, the discretization methods employed, the software and hardware optimizations involved, and the innovative algorithmic strategies used to push the limits of modern supercomputing resources.

Through this seminar, you will not only deepen your understanding of the latest advancements in high-performance computing but also gain practical knowledge of the methodologies and tools needed to carry out large-scale simulations on the world’s fastest supercomputers. By critically reviewing these papers, you will gain a comprehensive view of how computational scientists harness the full potential of supercomputing technologies to solve some of the most challenging problems across diverse scientific and engineering disciplines.

Subject: Geometric Deep Learning with Graph Neural Networks

The purpose of this part will be constructing and testing GNN architectures that can predict node-level probabilities in molecular graphs constructed from protein molecules. The ultimate goal of the project is to compare multiple equivariant SE3 architectures and multiple representations and node embeddings for a specific task of predicting protein pocket identification. More information are available here

Subject: Numerical methods for the nonlinear Schrödinger equation

The nonlinear Schrödinger equation can be derived in many physical contexts, and in particular as enveloppe equations for the propagation of waves in various media …. More information are available here