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.

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

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#### Advanced Machine Learning: Applications to Vision, Audio and Text

#### Advanced numerical methods for PDEs and optimal transport problems

#### An introduction to shape and topology optimization

#### Computational biology

#### Data Science Seminars and Challenge

#### Differential Calculus, Wavelets and Applications

#### Fluid mechanics and granular matter

#### From Basic Machine Learning models to Advanced Kernel Learning

#### Geophysical imaging

#### GPU Computing

#### Handling uncertainties in (large-scale) numerical models

#### Learning, Probabilities and Causality

#### Mathematical Foundations of Machine Learning

#### Mathematical Foundations of Machine Learning (new syllabus in 2025)

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

#### Mathematical optimization.

#### Modeling Seminar

#### Natural Language Processing & Information Retrieval

#### Natural Language Processing & Information Retrieval (new syllabus in 2025)

#### Numerical Mechanics

#### Quantum Information & Dynamics

#### Statistical learning: from parametric to nonparametric models

#### Temporal, spatial and extreme event analysis

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.

The goal of this course is to present and analyze a wide range of numerical methods and algorithms.

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).

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.

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

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.

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.

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

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.

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

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.

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

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

Theoretical foundations of convex optimization.

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

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

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

TApplied to both special effects in films and virtual prototyping in industry, physical simulation has become a powerful tool, …

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

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

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.