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# Seminars

The Departement of Mathematical Engineering organizes a series of seminars. The seminars are held in the Euler lecture room, Building EULER, av. Georges Lemaître 4-6, Louvain-la-Neuve (Parking 13).

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

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. |

02/10/2018 (14:00) [Lieu : Bât. Euler (room A.002)]Adrien Scheuer 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. Jefferys 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 Jefferys 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. |

27/11/2018 (14:00) [Lieu : Bât. Euler (room A.002)]Erik Bekkers (Eindhoven University of Technology) TBA |

TBA |

### Previous seminars

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. |