M2 SIAM program

Tracks during fall semester 2024

The first semester of MSIAM master 2 is essentially divided in two tracks. Each student should be registered in one of the following tracks:

However a personalized track may also be build for some students from the available courses (if no timetable conflicts appears). The personalized tracks must be approved by the Professors in charge of MSIAM.

Academic program

  • 30 ECTS scientific courses (3 or 6 each, excluding French language course).
*

Advanced Machine Learning: Applications to Vision, Audio and Text

The objective of this course is to provide the principles of advanced (supervised and unsupervised) machine learning algorithms, and explain their interest when applying them to address learning tasks using visual, auditory or textual data, as well as multi-modal combinations.

An introduction to shape and topology optimization

In a very broad acceptation, shape and topology optimization is about finding the best domain (which may represent, depending on applications, a mechanical structure, a fluid channel,…) with respect to a given performance criterion (e.g. robustness, weight, etc.), under some constraints (e.g. of a geometric nature).

Computational biology

This interdisciplinary course is designed for students with a computer science or mathematical background, offering them an opening to bioinformatics and to bioinformatics and computational biology.

Data Science Seminars and Challenge

This course consists on a cycle of seminars given by different industrials and on a projet related to the manipulation of real data.

Differential Calculus, Wavelets and Applications

The course is structured in two parts, treated respectively and independently by Sylvein Meignen and Kévin Polisano. The first part is devoted to differential calculus and its applications in image restoration and edge detection. The second part is dedicated to the construction and practical use of the wavelet transform. Wavelets are basis functions widely used in a large variety of fields: signal and image processing, data compression, smoothing/denoising data, numerical schemes for partial differential equations, scientific visualization, etc. Connections between the two parts will be made on the aspects of denoising, edge detection and graph analysis.

Efficient methods in optimization

Theoretical foundations of convex optimization.

Fluid mechanics and granular matter

Equations and models are presented in a continuum setting, and then approximated in time and space. Then, the efficient numerical resolution is addressed with some examples of practical applications.

From Basic Machine Learning models to Advanced Kernel Learning

Statistical learning is about the construction and study of systems that can automatically learn from data.

Geophysical imaging

In the current context of energy transition and fight against global warming, a precise knowledge of the crust, down to several km depth, has become a critical issue.

GPU Computing

In this course, we will introduce parallel programming paradigms to the students in the context of applied mathematics.

Handling uncertainties in (large-scale) numerical models

Numerical simulation is ubiquitous in today’s world. Initially confined to well-mastered physical problems, it has spread to all fields (oceanography, biology, ecology, etc.), the aim being to make forecasts of the systems under study.

Learning, Probabilities and Causality

The main aim of this course is to provide the principles and tools to understand and master learning models based on probabilities and causality.

Mathematical Foundations of Machine Learning

Understanding of fundamental notions in Machine Learning (inference, ERM and SRM principles, generalization bounds, classical learning models, unsupervised learning, semi-supervised learning.

Modeling Seminar

This lecture proposes modelling problems. The problems can be industrial or academic.

Natural Language Processing & Information Retrieval

The automatic processing of languages, whether written or spoken, …

Optimal transport: theory, applications and related numerical methods.

The goal of this course is to present a wide range of recent numerical methods and algorithms that find applications in various fields. More precisely, the course will focus on optimal transport algorithms, proximal methods and level set methods – the leading application of these being image analysis.

Quantum Information & Dynamics

The quantum formalism developed a century ago provides a very precise description of nature at small scales which entails several counter intuitive aspects, …

Software Development Tools and Methods.

This lecture presents various useful applications, libraries and methods for software engineering related to applied mathematics.

Statistical learning: from parametric to nonparametric models

This course is related to mathematical and statistical methods which are very used in supervised learning.

Temporal, spatial and extreme event analysis

Modelling extreme temperatures, extreme river flows, earthquakes intensities, neuronal activity, map diseases, lightning strikes, forest fires, for example is a risk modelling and assessment task, which is tackled in statistics using point processes and extreme value theory.