The first semester of MSIAM master 2 is essentially divided into two tracks. Each student should be registered in one of the following tracks:
However a personalized track may also be built for some students from the available courses (if no timetable conflicts appear). The personalized tracks must be approved by the Professors in charge of MSIAM.
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 computational biology.
This course consists of a cycle of seminars given by different industrial speakers and of a project related to the manipulation of real data.
The course is structured in two parts, treated respectively and independently by Sylvain 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.
Statistical learning is about the construction and study of systems that can automatically learn from data.
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.
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.
The main aim of this course is to provide the principles and tools to understand and master learning models based on probabilities and causality.
Machine learning methods for physical modelling: physics-informed neural networks, neural operators, convexity-preserving networks, and their comparison with classical numerical solvers.
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 quantum formalism developed a century ago provides a very precise description of nature at small scales which entails several counterintuitive aspects, …
This course is related to mathematical and statistical methods which are widely used in supervised learning.
This MSc course aims at presenting the fundamental concepts of Stochastic Calculus
Modelling extreme temperatures, extreme river flows, earthquake intensities, neuronal activity, disease maps, 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.