Visioconférence, 14h00 Virtual meeting, 2:00 PM
Multicomponent signals (MCSs) enable to accurately represent non-stationary signals in many fields, for instance, in pathology diagnosis, structural damage or physiological signals. Mode retrieval techniques aim to obtain the instantaneous frequency (IF) and instantaneous amplitude (IA) information from the MCSs. The technique we consider is designed to avoid mode mixing by using information from the ridge of the time frequency (TF) region associated with each mode. This approach is also interesting in the noisy case as it only considers a small part of the mode's TF region. |
Bâtiment IMAG, salle 106, 10h00 IMAG building, room 106, 10:00 AM
Multistage Stochastic Programming consists in minimizing the expected cost of some decision over a set of coupled scenarios. Progressive Hedging is a popular strategy for solving such problems, based on scenario decomposition. In this talk, we present a randomized version of this algorithm able to compute an update as soon as a scenario subproblem is solved. This is of crucial importance when run on parallel computing architectures. We prove that the randomized version has the same converge properties as the standard one and we release an easy-to-use Julia toolbox. |
Bâtiment IMAG, salle 106, 15h30 IMAG building, room 106, 3:30 PM
Extreme precipitation may cause important flood that can induce huge damage. Rainfall are subject to local orography features and their intensities can be highly variable. In this context, identifying climatologically coherent regions is paramount to increase any signal strength, e.g. with respect to climate change, in precipitation data. To gather stations into homogeneous
regions, Hosking (1985) introduced the concept of Regional
Frequency Analysis. RFA is based on clustering weather
stations according to their rainfall marginal distributions.
One limiting assumption in the RFA approach is the need to
specify a parametric form for the marginal distributions,
up to a normalizing factor.
We combine this threshold-free approach with RFA techniques. |
Bâtiment IMAG, Salle 106, 15h
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Bâtiment IMAG, Salle 106, 15h30
Neural networks (NNs), and their deep counterparts, have largely been used in many research areas such as image analysis, signal processing, or reinforcement learning, just to name a few. The impressive performance provided by such machine learning approaches has greatly motivated research that aims at a better understanding the driving mechanisms behind their effectiveness. In particular, the study of the NNs distributional properties through Bayesian analysis has recently gained much attention. In this seminar we firstly describe the necessary notations and statistical background for Bayesian NNs. Then we consider its distributional properties and novel theoretical insight on distributions at the units level. Under the assumption of independent and normally distributed weights, we establish that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. Lastly, we discuss this property in terms of a regularizing mechanism and corroborate it with experimental simulation results. |
Bâtiment IMAG, Salle 106, 15h30
The dynamic of sediments flow is a subject that covers many applications in geophysics, ranging from estuary silting to the comprehension of sedimentary basins. In this seminar we will see how to implement a high performance direct numerical solver for the resolution of fluid dynamics applied to sedimentation problems where the sediment flow contain multiple interacting fluid phases. In this second part we will introduce the sedimentation problem and its discretization. The Navier-Stokes equations will be coupled with two additional advection-diffusion equations modelling the transport of two scalars representing the sediment phases. We will then take a close look to the interactions which lead to several instabilities (Rayleigh-Taylor instabilities and double-diffusivity). We finish by comparing the results to the state of the art. 
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Bâtiment IMAG, Salle 106, 15h30
The dynamic of sediments flow is a subject that covers many applications in geophysics, ranging from estuary silting to the comprehension of sedimentary basins. In this seminar we will see how to implement a high performance direct numerical solver for the resolution of fluid dynamics applied to sedimentation problems where the sediment flow contain multiple interacting fluid phases. In this first part we will introduce the HySoP library, a framework that combines efficient numerical methods running on distributed hybrid CPU-GPU computing platforms. This framework allows us to solve efficiently multiple 2D and 3D fluid problems by discretizing and splitting the Navier-Stokes equations. Several numerical results will be shown. 
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Bâtiment IMAG, salle séminaire 1, 15h
In this seminar, we show how optimal transport theory can be used to build a common framework to solve many optical component design problems. In a first part, we present optimal transport, its main formulations and the motivations behind it. We then describe in more details the so-called semi-discrete setting where the target measure is supported on a point cloud and explain the main numerical method we will use namely the damped Newton's algorithm. We then look at a particular case where the source measure is supported on a triangulation in R^3 and show the convergence with linear speed of the damped Newton's method. The convergence is a direct consequence of the regularity and strict motonicity of the Kantorovich functional. We also mention some applications such as optimal quantization of a probability density over a surface or remeshing. In a second part, we describe the relation between optimal transport and optical component design. In particular, we show how we can recast such problems into a non-linear system of equations that is a discretization of the so-called Monge-Ampère equation. This formulation allows us to develop a generic, parameter-free and efficient algorithm. We finish by showing numerous simulated and fabricated examples. |
Bâtiment IMAG, salle 118, 15h30
Bâtiment IMAG, salle 106, 16h00
Many physical phenomena are modelled numerically in order to better understand and/or to predict their behaviour. However, some complex and small scale phenomena can not be fully represented in the models. The introduction of ad-hoc correcting terms is usually the solution to represent these unresolved processes, but those need to be properly estimated. A good example of this type of problem is the estimation of bottom friction parameters of the ocean floor. This task is further complicated by the presence of uncertainties in certain other characteristics linking the bottom and the surface (eg boundary conditions). Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. The optimum is directly dependent on the fixed nominal value given to the uncertain parameter ; and therefore may not be relevant in other conditions. Strategies taking into account those uncertainties will be presented and applied on an academic model of a coastal area, in order to find an optimal value in a robust sense. Under the supervision of: Élise Arnaud, Laurent Debreu, Arthur Vidard. Keywords: Robust optimisation ; Bayesian inference ; Design of computer experiments ; multiobjective optimisation |
Bâtiment IMAG, salle 106, 16h00
In 2012, a collaboration between TOTAL E&P, ISTerre and the LJK has been launched on the study of sea ice mechanics. They developed a granular model for sea ice modeling. We want to improve this model by taking into account percussion and fracturation of ice floes. We will start by sketching our model for the fracturation of a single ice floe submitted to a displacement of it's boundary. We consider our ice floe as an elastic material. According to Griffith's criterion, finding the fracture's location amounts to minimizing an energy functional on the right functional space. We justify our modeling method with a Gamma-convergence result. Then, we will describe our strategy to understand the percussion mechanism. Oddly enough, there is no theory for the percussion of two elastic materials. We will present a gamma-convergence result that allows us to go from the microscopic scale to the macroscopic scale. That result is the fist step to retrieve macroscopic effects from a microscopic scale description of percussion. |
Bâtiment IMAG, salle 106, 15h30
Beaucoup d'applications nécessitent des simulations couplant modèle d'océan et d'atmosphère. Par exemple les modèles numériques de climat sont des outils indispensables pour anticiper les risques futurs dus au changement climatique. Actuellement ces modèles présentent des incertitudes liées notamment à des aspects mathématiques des algorithmes. Dans ce contexte nous cherchons à améliorer ces algorithmes et les algorithmes de Schwarz utilisés dans la décomposition de domaine sont de bons candidats. Dans le cadre de mon stage de M2 nous avons étudié la convergence théorique et numérique de ces algorithmes de Schwarz appliqués à des problèmes simplifiés de couplage océan-atmosphère. Plus précisément nous avons étudié la convergence des algorithmes de couplage sur des équations de type diffusion sur des domaines finis et pour des coefficients de diffusion pas nécessairement constants. |
Bâtiment IMAG, salle 106, 15h30
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Bâtiment IMAG, salle 106, 15h30
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