The Departement of Mathematical Engineering organizes a series of seminars. The seminars are usually held on Tuesday from 2:00pm to 3:00pm in the Euler lecture room, Building EULER, av. Georges Lemaître 4-6, Louvain-la-Neuve (Parking 13). Be mindful that exceptions may occur; see the talk annoucements.

If you wish to receive the seminar announcements by email, please send an email to Etienne Huens.

Master students can take this seminar for credit in either of the two semesters; see LINMA2120 for more information.

Seminars to come

05/02/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Silvia Villa (Università di Genova)
Iterative regularization using proximal methods

In the context of linear inverse problems, I will discuss iterative regularization methods allowing to consider large classes of data-fit terms and regularizers.In particular, I will investigate regularization properties of first order proximal splitting optimization techniques. Such methods are appealing since their computational complexity is tailored to the estimation accuracy allowed by the data, as I will show theoretically and numerically.

19/02/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Jesús Angulo (CMM-Centre de Morphologie Mathématique, MINES ParisTech, PSL-Research University, France)
Minkowski Set Operations and Morphological Openings of Ellipsoids - Application for Processing Positive Definite Matrix-Valued Images

Morphological dilation and erosion for sets are based on (geometric) Minkowski sum and difference of two sets. In this talk we deal with the particular case of ellipsoids. Indeed ellipsoidal sets appear nowadays in different image and data representations, e.g., in diffusion tensor imaging each voxel is valued with a 3D ellipsoid; the dispersion of a scatter set of points can be described by a multivariate Gaussian distribution where the covariance matrix may be seen as ellipsoidal shape centered at the mean position. The Minkowski sum and difference of two ellipsoidal sets are in general not ellipsoidal. However, in many applications, we are interested in computing the ellipsoidal set which approximates in a certain sense the Minkowski operations.
A closed-form characterization of Minkowski operations of two ellipsoids has been recently introduced (Yan and Chirikjian, 2015), which provide implicit surface expression and parametric formulas for the boundary of the Minkowski sum and difference of two arbitrary oriented ellipsoids. We adopt in this study a different approach based on the so-called ellipsoidal calculus (Kurzhanski and Valyi, 1996). Ellipsoidal calculus is a method for solving problems in control and estimation theory having unknown but bounded errors in terms of sets of approximating ellipsoidal-value functions.
Using the theory and algorithms from ellipsoidal calculus, we consider parameterized families of external and internal ellipsoids that tightly approximate the Minkowski sum and difference of ellipsoids. Approximations are tight along a direction l in the sense that the support functions on l of the ellipsoids are equal to the support function on l of the sum and difference. External (resp. internal) support function-based approximation can be then selected according to minimal (resp. maximal) measures of volume or trace of the corresponding ellipsoid. We focus in particular on the ellipsoidal approximations to the morphological opening between two ellipsoids and its interest in practical examples.
We discuss also the connection between the approximations to the Minkowski sum and difference of two positive definite matrices and their mean using their Euclidean or Riemannian geometries, which is also related to their Bures-Wasserstein mean (Bhatia et al., 2018).

Bhatia R., Jain T., Lim Y. (2018) On the Bures-Wasserstein Distance Between Positive Definite Matrices. Expositiones Mathematicae, to appear.
Kurzhanski A.B, Valyi I (1996). Ellipsoidal Calculus for Estimation and Control. Birkhäuser, Boston, MA, 1996.
Mazure M.-L (1991) Equations de convolution et formes quadratiques. Annali di Maematica pura et applicata (IV), Vol. CLVIII, 75-97.
Yan Y, Chirikjian G.S (2015) Closed characterization of the Minkowski sum and difference of two ellipsoids. Geom. Dedicata 177:103-128.

26/02/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Mohamed Daoudi and Anis Kacem (IMT Lille Douai)

05/03/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Alexandre Bovet (UCLouvain)

12/03/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Laurent Jacques (UCLouvain)

19/03/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
James Mathew (UCLouvain)

26/03/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Felix Lieder (Universität Düsseldorf)

02/04/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Erling Andersen (CEO of MOSEK)
A primal-dual interior-point algorithm for nonsymmetric conic optimization

30/04/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Benoit Delhaye (UCLouvain)

07/05/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Mihai Cucuringu (University of Oxford)

14/05/2019 (14:00) [Lieu : Bât. Euler (room A.002)]
Tsiaflakis Paschalis (Nokia Bell Labs, Antwerp)
Signal processing and optimization for ultrabroadband internet access

Previous seminars

18/12/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Zheming Wang (UCLouvain)
Computation of the maximal invariant set of discrete-time systems with quasi-smooth nonlinear constraints

Invariant set theory is an important tool for stability analysis and control design of constrained dynamical systems and it has been successfully used to solve various problems in system and control. In this talk, we study the computation of the maximal invariant set of linear systems with a class of nonlinear constraints that has quadratic relaxations. With these quadratic relaxations, we are able to determine a sufficient condition for the maximal invariant set. By using the sufficient condition, we propose an algorithm to compute the exact maximal invariant set. At each iteration, we will solve a set of linear matrix inequalities instead of a nonlinear optimization problem. Thanks to this feature, the proposed algorithm is computationally tractable and efficient in many cases. Under mild assumptions, the proposed algorithm will terminate in finite time. This algorithm can also be extended to a class of nonlinear systems that admit a state feedback linearization. The performance of this algorithm is demonstrated on several numerical examples.

12/12/2018 (16:30) [Lieu : Bât. Euler (room A.002)]
Colin Jones (EPFL)
Predictive Dispatch and Demand Response for Commercial Buildings

Note the unusual day (Wednesday).
Commercial buildings have significant flexibility in how and when they consume energy, and this freedom can be put to good use by grid operators managing the stability of the grid. This talk will discuss demand response for buildings, or the throttling of power consumption in reaction to signals sent by the grid operator. By shifting energy consumption in time, these techniques can be seen as utilizing the thermal inertia of buildings as a form of virtual electrical storage. In the first part of the talk, we will introduce and analyse a hybrid storage system that combines the best properties of electrical batteries, commercial buildings and generation re-scheduling to better provide balancing services at multiple time scales. We will then demonstrate the effectiveness of the proposed control framework via a set of 12 full day experimental results on the 20kV distribution feeder of the EPFL campus that is comprised of: a set of five uncontrollable office buildings (350kWp) and a roof-top PV installation (90kWp), and a set of controllable resources: a grid-connected BESS (720kVA-500kWh), and a small occupied office building (45 kWp).

04/12/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Guillaume Berger and Benoît Legat (UCLouvain)
Two 20-minute talks

Speaker: Guillaume Berger
Title: Path-complete p-dominant switching linear systems
Abstract: In this presentation, we study the asymptotic properties of a class of dynamical systems called switched linear systems. Therefore, we introduce the notion of path-complete $p$-dominance for switched linear systems as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional asymptotic behavior, and hence allow for a simplified analysis of their dynamics. Finally, we present an algorithm for deciding the path-dominance of a given system.

Speaker: Benoît Legat
Title: Minimally Constrained Stable Switched Systems and Application to Co-simulation
Abstract: We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by co-simulation of complex dynamical systems by multiple cores. There, numerical stability is a hard constraint, but should be attained by restricting as few as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.

27/11/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Erik Bekkers (Eindhoven University of Technology)
An introduction to sub-Riemannian geometry in SE(2) for vessel analysis and roto-translation equivariant deep learning

This presentation focusses on the application of sub-Riemannian geometry and group theory in 2D medical image analysis. In the discussed image analysis applications, 2D images are lifted to 3D functions on the coupled space of positions and orientations. Lifting is done via a (learned) wavelet-type transformation, leading to a neat organization of image data based on position and orientation. In the extended domain, which we identify with the Lie group SE(2), a sub-Riemannian (SR) geometry is recognized. Here, "sub" refers to the restriction that tangent vectors of naturally lifted curves are contained in a sub-space of the full tangent space. A parallel can be drawn between these curves and the paths of moving cars: a car can only move forward and change direction (2 controls) in a 3D state-space (2D position and orientation), but is not able to move sideways.

In this presentation the following items are discussed:
- A introduction to the Lie group SE(2) (group product, algebra, exponential/logarithmic map and representations)
- An explanation of the sub-Riemannian geometry on SE(2)
- The benefit of using sub-Riemannian geometry for vessel tracking
- The benefit of using the Lie group structure of SE(2) for equivariant or invariant deep learning

13/11/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Thanh Son Nguyen (UCLouvain)
Parametric model order reduction and interpolation on matrix manifolds as a tool

Large-scale control systems appear frequently as mathematical models for many practical fields such as heat conduction, electrical circuits. Simulation of such systems requires solving equations whose order can reach dozen of thousands. Besides, in many cases, these systems depend on parameter which makes the simulation more challenging. In this talk, first we will give an introduction to model order reduction of parameter-dependent linear time-invariant systems as well as a review of interpolation-based methods. Then we will explain why in some cases, we have to do it in the framework of interpolation on matrix manifolds. Finally, we will present some numerical examples for illustrative purpose.

06/11/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
New PhD students in INMA
Welcome Seminar #2

In this seminar, new PhD students in INMA will introduce themselves and their research topic: "Compressive Learning : learning from 'too much' data" (Vincent Schellekens); "Signal processing for direct imaging of stellar systems" (Benoît Pairet); "Optimal interference nulling for large arrays of coupled antennas" (Valentin Hamaide); "Algorithms for smart content marketing" (Mridul Seth).

23/10/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Laurent Demanet (Departments of Mathematics and EAPS, MIT)
Interferometry and convex programming

A number of hard estimation questions in science and engineering can be expressed as recovering a rank-1 matrix from linear measurements. One example that I will cover in this talk is "interferometry", a trick in signal processing and imaging consisting in taking cross-correlations to attenuate incoherent noise. I show that recovery for inverse problems involving interferometric combinations is sometimes possible with varying levels of convex relaxations, and depends on the underlying graph of measurements being an expander. I also show an example of "interferometric thinking" to blind deconvolution, where it enables the design of new sparse regularizers.

16/10/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
New PhD students in INMA
Welcome Seminar #1

In this seminar, new PhD students in INMA will introduce themselves and their research topic: "Nonnegative matrix factorization in infinite-dimensional feature spaces : a parameterized approach" (Cécile Hautecoeur); "Analysis and Control of Interconnected Systems" (Ayoub Ben Ayed); "Decentralized optimization in open multi-agent systems" (Charles Monnoyer); "MILP-based Algorithm for the Global Solution of Economic Dispatch Problems with Valve-Point Effects" (Loïc Van Hoorebeeck).

09/10/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Jean-François Cardoso and Pierre Ablin (CNRS - INRIA)
Fast and invariant learning for Independent Component Analysis

Independent Component Analysis (ICA) is a widely used unsupervised data exploration technique. It models a set of observed signals as a linear mixtures of statistically independent sources and aims at recovering blindly those underlying sources. Here `blind' means that sources are recovered from the signals by applying a separating matrix which is totally inconstrained, making ICA applicable in a large variety of tasks. After a brief introduction, we stress the multiplicative structure of the ICA problem: the parameter space is the multiplicative group of GL(n) of square invertible matrices. Learning algorithms which exploit this structure are `equivariant' and are `rewarded' for doing so in terms implementation, optimization and performance, as we shall see. In a second part, we introduce a fast quasi-Newton equivariant algorithm for ICA, the Preconditioned ICA for Real Data (Picard) algorithm. It exploits the specific structure of the problem to compute cheap Hessian approximations, and then refines them using L-BFGS, a classical optimization algorithm. It shows state of the art convergence speed when applied to real datasets. Interestingly, it can be straightforwardly constrained to work on the rotation manifold, a constraint often imposed in ICA.

02/10/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Adrien Scheuer (UCLouvain)
Multi-scale modelling of fibre suspensions: Particle inertia, confined flows and data-driven approach

Suspensions of fibres and non-spherical particles are encountered in many fields ranging from engineering to biology, e.g. papermaking, composite manufacturing, pharmaceutical applications, red blood cells, food-processing and cosmetics industries, etc. Predicting the evolution of the orientation state of the particles is crucial to estimate the rheology of the suspension, that is its flow behaviour, as well as the final properties of the material. Jeffery’s theory, describing the kinematics of a single particle immersed in an homogeneous flow of Newtonian fluid, lays the foundation for almost every models used today. Coarser representations, built upon this work, have been introduced later to describe statistically the orientation state of the particles, either using a probability density function, or even moments of this function (Advani-Tucker orientation tensors). The assumptions underlying Jeffery’s model are however quite restrictive to predict reliably what happens in fibre suspensions flows encountered in industrial processes. In this thesis, we first revisit this model, studying the impact of particle inertia and of confinement (wall effects) on the particle kinematics. In each case, we propose a multi-scale approach, but given the challenges to upscale the microscopic description to the macroscopic scale, we then came up with an innovative approach based on data-driven simulations to circumvent upscaling issues and inaccuracies introduced by macroscopic closure approximations. Finally, we developed efficient numerical methods to simulate fluid flows in thin geometries, considering, within the Proper Generalized Decomposition (PGD) framework, an in-plane/out-of-plane separated representation of the solutions of the incompressible Navier-Stokes equations.

25/09/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Elarbi Achhab (Université Chouaïb Doukkali)
Compensator Design for a class of Infinite-Dimensional Semilinear Systems

In this talk, we consider a class of partially observed infinite-dimensional semi-linear systems. First, we address the problem of the design of an exponential Luenberger-like observer for this class of systems. Then, using the state estimation result stated, a stabilizing compensator for this class of systems will be designed. A compensator is an auxiliary system which has as its input the output of the initial system and as its output the input of the original one. In our setting, the obtained control law is showed to exponentially stabilize around a desired equilibrium profile the system under consideration. Finally, the main result is applied to a non isothermal chemical plug flow reactor model. The approach is illustrated by numerical simulations.

18/09/2018 (14:00) [Lieu : Bât. Euler (room A.002)]
Antoine Godin (Agence Française de Développement)
The Stock-Flow Consistent approach or the importance of disequilibrium

Stock-Flow Consistent (SFC) models are sectoral macroeconomic models that combine two fundamental insights: first, the economy is ruled by imbalances and its reactions to these imbalances, and second, the economy is a dynamical multi-layered network of financial relationships. By combining these two aspects, SFC models are a powerful tool to understand modern financialised economies in modelling feedback loops between exchanges of good and services, financial flows, and wealth. The GEMMES research project at the French Agency for Development aims at contributing to the international debate related to climate change (both for the adaptation and mitigation aspects). Given the importance and the pervasive aspect of the transition to a low carbon economy, it is fundamental to be able to grasp how it will re-shape, create or steer imbalances and hence might lead to unsustainable dynamics such as financial crisis. This seminar will go through three different modelling approaches, all using the insight of Stock-Flow Consistency, to show the importance of disequilibrium and imbalances in economics

11/09/2018 (16:30) [Lieu : Core(room b.135)]
Ion Necoara (Univ.Pol.Bucharest)
Stochastic algorithms for convex feasibility and convex minimization

In this talk we present stochastic first-order methods for solving convex feasibility problems or convex minimization problems with many constraints. First, for the convex feasibility problem (that is finding a point in the (in)finite intersection of convex sets) we propose several equivalent stochastic reformulations, such as stochastic (non)smooth optimization problem, stochastic fixed point problem, or stochastic intersection problem. Based on these reformulations and on new characterization of the conditioning parameters we introduce a general random projection algorithmic framework with an over-relaxed stepsize, which generates either new algorithms or extends to random settings many existing alternating projection schemes. We also derive (sub)linear convergence rates for this general algorithm that depend explicitly on the conditioning parameters and on the number of projections computed at each iteration. Then, we extend this stochastic algorithmic framework to convex minimization problems subject to (in)fi nite intersection of constraints. For this algorithm we also derive convergence rates in terms of the expected quadratic distance from the iterates to the optimal solution for smooth strongly convex objective functions, which in the best case is of order O(1/k). We also provide necessary and sufficient conditions for linear convergence of this stochastic method. Finally, we give examples of several functional classes satisfying our new conditions and discuss several applications of these results.

4/09/2018 (14:00) [Lieu : Bât. Euler (room A.207)]
Sebastian Stich (EPFL)
Communication Efficient Variants of SGD for Distributed Computing

Nowadays machine learning applications require stochastic optimization algorithms that can be implemented on distributed systems. The communication overhead of the algorithms is a key bottleneck that hinders perfect scalability. In this talk we will discuss two techniques that aim reducing the communication costs. First, we discuss quantization and sparsification techniques that reduce the amount of data that needs to be communicated. We present a variant of SGD with k-sparsification (for instance top-k or random-k) and show that this scheme converges at the same rate as vanilla SGD. That is, the communication can be reduced by a factor of the dimension of the whilst still converging at the same rate. In the second (and shorter) half of the talk we discuss strategies that tackle the communication frequency instead of the communicated data. In particular, we compare local SGD (independent runs of SGD in parallel) with mini batch SGD.