All Years Seminars
[INMA] 2019-11-26 (14:00) : Some geometric and machine learning methods for model order reduction
At Euler building (room A.002)
Speaker :
Rolando Mosquera (LaSIE, Université de la Rochelle, France
)
,
and
Antoine Falaize (LaSIE, Université de la Rochelle, France
)
Abstract :
Geometric methods have proved to be effective for data mining (simulations, measurements) in the context of nonlinear model order reduction problems in mechanics (e.g. nonlinear methods for dimensionality reduction such as Local Principal Component Analysis, LPCA or Locally Linear Embedding, LLE). In addition, deep learning methods by so-called neural network (NN) architectures proved to be effective for a class of problems involving data classification, detection and compression.
We first present a set of geometric tools for the interpolation of reduced bases obtained by orthogonal decomposition (POD) of simulation results. More precisely, by exploiting the intrinsic geometry of the sub- spaces engendered by the POD bases, we give the construction of different interpolators on the Grassmann manifold.
Then, we use the architecture of neural networks to extract geometric informations about the data manifold. More precisely, a metric on the manifold can be found from the representations of coordinates learned by the network. Conversely, classical architectures of neural networks can be informed by the geometry of the data to build optimizers that respect the local geometry. These approaches are illustrated on model order reduction problems in mechanics.
[INMA] 2019-11-19 (14:00) : Parameter identification in elliptic PDEs from boundary data: finite element method with total variation regularization
At Euler building (room A.002)
Speaker :
Tran Nhan Tam Quyen (Institute for Numerical and Applied Mathematics, University of Goettingen, Germany.)
Abstract :
In this presentation we would like to present the problem of identifying the conductivity and the source term in elliptic PDEs from several sets of boundary data. The finite element method with total variation regularization technique is applied to tackle the ill-posed identification problem. We analyze the stability of the proposed approach and the convergence of the finite element regularization approximations to the sought parameters, which confirm that the parameters distributed inside the physical domain can be reconstructed from a finite number of observations on the boundary.
[INMA] 2019-11-12 (14:00) : Control synthesis for large collections of dynamical systems with counting constraints
At Euler building (room A.002)
Speaker :
Necmiye Ozay (Univ. Michigan, USA)
Abstract : Can we control a swarm of systems and give guarantees on their collective behavior? In this talk I will discuss an instance of this problem: given a large almost homogeneous collection of dynamical systems and a novel class of safety constraints, called counting constraints, how to synthesize a controller that guarantees the satisfaction of these constraints. Counting constraints impose restrictions on the number of systems that are in a particular mode or in a given region of the state-space over time. I will present an approach for synthesizing correct-by-construction controllers to enforce such constraints. Our approach exploits the structure of the problem, the permutation invariance of dynamics due to homogeneity and the permutation invariance of counting constraints, to achieve massive scalability. I will discuss several potential applications of this approach and illustrate it on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.
[INMA] 2019-11-05 (14:00) : Two 20-minute talks
At Euler building (room A.002)
Section 1: Convex optimization using tunable first-order inexact oracles (TFOIO)
Speaker :
Van Dessel, Guillaume
Abstract : In this talk will be introduced/ motivated the concept of tunable first-order inexact oracle (TFOIO) in convex optimization.
More specifically: It will be first discussed convergence results for
smooth-convex optimization methods such as (P)GD and FGD taking
into account for inexactness both in the information used
(tunable first-order inexact oracle built upon surrogates for
the objective function and its (sub)gradient) and the accuracy
on the update steps. Then it will be shown how and when it is possible to derive, based on a cost (either computational or economical) associated with oracle calls, optimal schedules for the above methods. Worst-case cost gains will be presented for a proper set of chosen experiments.
Finally, if the time allows it, practical examples using a personal
toolbox will be displayed in live to confirm the empirical
behavior of the cited methods under the use of inexact
information.
Section 2: New developments in Machine Learning: a Kolmogorov Complexity approach
Speaker :
Pinon, Brieuc
Abstract : We first identify some intrinsic limitations in currently used learning algorithms in Machine Learning. These algorithms lack of learning automatization and expressiveness in order to efficiently exploit some structures in some complex tasks.
A solution can be found within the Kolmogorov Complexity framework, "perfect" learning that exploits all computable patterns in the data exists.
However, it is non-computable.
We point to potential practical solutions for this problem, and theoretical questions that we investigate.
An understanding of introductory notions in Machine Learning and Theoretical Computer Science is advised.
[INMA] 2019-10-29 (14:00) : Gait parametrization and limit cycle stability of flapping bird flight
At Euler building (room A.002)
Speaker :
Gianmarco Ducci (UCLouvain (IMMC))
Abstract :
The biomechanics of birds is of crucial interest for modern engineering applications. Indeed, flapping birds display the ability of maintaining a stable flight in a continuously perturbed environment, while executing complex maneuvers.
We developed a method identifying trimmed flight conditions for flapping wings. These particular conditions correspond to limit cycles in the state space domain, with the same period as the flapping input. Our method is based on a multiple-shooting algorithm that can simultaneously identify unknown limit cycles of the longitudinal equations of bird s motion, and assess its stability relying on Floquet theory.
This framework further employs a lifting line aerodynamic model developed in the group of fluid mechanics at UCLouvain. Consequently, sensitivity analysis of gait configurations as a function of the wing kinematic parameters can be conducted.
Results suggest that birds should continuously rely on feedback control scheme to achieve steady-state flapping flight, and possible solutions to achieve such flight stabilization are discussed.
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