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 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.
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.
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.