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.

Please note that from now and until further notice, comodal participation will be possible via this link : O365G-cours-linma2120-seminars.

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

07/12/2021 (14h) [Location: Euler building (room a.002)]
Pierre Ablin (Université Paris-Dauphine)
The symbiotic relationship between optimization and deep learning

Abstract: Optimization is one of the cornerstones of deep learning: most deep neural networks are trained by optimizing a cost function. The purpose of this talk is to cover other fruitful interactions between the fields of optimization and deep learning that are less obvious. First, I will discuss how deep neural networks can be designed to quickly and efficiently solve classical optimization problems, with a focus on the Lasso. I will then argue that the tools of optimization allow us to describe accurately what weights are learned by these networks during the training process. In a second part, I will discuss how classical optimization ideas like momentum acceleration can be translated to deep learning, and allow us to develop novel architectures that perform well and are memory-efficient.

Previous seminars

30/11/2021 (14h) [Location: Euler building (room a.002)]
Geovani Nunes Grapiglia (UCLouvain/INMA)
A Generalized Worst-Case Complexity Analysis for Non-Monotone Line Searches

Abstract: In this talk we discuss the worst-case complexity of a wide class of non-monotone line search methods for non-convex unconstrained minimization problems. For the algorithms in this class, the non monotonicity is controlled by a sequence of nonnegative parameters. We prove complexity bounds to achieve approximate first-order optimality even when this sequence is not summable. As a by-product, we obtain a unified global convergence result. Our generalized results allow more freedom for the development of new non-monotone line search algorithms. As an example, we design a non-monotone scheme related to the Metropolis rule. Preliminary numerical experiments suggest that the new method is suitable to nonconvex problems with many non-global local minimizers.

23/11/2021 (14h) [Location: Euler building (room a.002)]
Flavio Abreu Araujo (UCLouvain)
Implementing spintronic based neuromorphic computing hardware under the reservoir computing approach

Abstract: The brain displays many signatures of non-linear dynamical behavior, including synchronization and complex transient behavior. These observations have inspired a whole class of neuromorphic concepts based on complex networks of interconnected non-linear nodes. Such non-linearity has been identified as one of the main ingredients to achieve excellent performance in cognitive tasks such as spoken digit recognition. In this work, we have quantified in detail the contribution of the acoustic filtering and the neural network, respectively, for spoken digit recognition task using three different frequency decomposition methods: Cochlear, MFCC and Spectrogram. In a first step, we have demonstrated that Cochlear and MFCC are powerful stand-alone features extractors, and they can achieve for themselves very high recognition level: up to 95.8% and 77.2% for cochlear and MFCC, respectively. We have found that such high recognition level is mainly due to the non-linear character of these frequency decomposition methods. First, we have investigated the non- linear dependence of the Spectrogram showing a huge increase of recognition rate from 10% (linear) to 85.6%. In a second step, we have evaluated the gain of the recognition rate provided by the neural network. For simplicity, we have modeled a neural network based on the non- linear dynamics of oscillators in the framework of the reservoir computing approach. The reservoir is generally composed by a large number of fixed and random interconnected non- linear oscillators which generates very complex non-linear dynamics. The key insight behind reservoir computing is that only the external connections (between the reservoir and the output layer) should be trained to obtain the desirable target. Reservoir computing has been identified to be very suitable for different hardware implementations: optical, photonic and spintronic devices. We have found that the contribution of the neural network is dominant for the linear Spectrogram filter but not in the other two cases, i.e., cochlear and MFCC. Finally, we have carried out experiments using non-linear and tunable spin-torque nano-oscillators exhibiting an excellent agreement with our simulations.

16/11/2021 (14h) [Location: Euler building (room a.002)]
Radu Dragomir (UCL/INMA)
Gradient methods with Bregman distances

Abstract: Large-scale optimization problems from signal processing and machine learning are typically solved with gradient methods, because of their low cost per iteration and their simplicity. In this talk, we study a generalization of the standard gradient descent, which consists in replacing the Euclidean distance by a more general Bregman divergence induced by some simple convex reference function. This function is chosen to be adapted to the geometry of the problem at hand through the so-called relative smoothness condition. We present some advances in this recent line of work, including the study of worst-case complexity through performance estimation problems (PEPs), as well as applications to low-rank matrix optimization.

09/11/2021 (14h) [Location: Euler building (room a.002)]
Renato Vizuete (CentraleSupélec and GIPSA-lab, France )
Graphons for the Estimation of Performance Indices in Large Networks

Abstract: In recent years, the analysis of large networks has received increasing attention in many scientific fields due to the continuous evolution of the world towards a networked environment with a large number of connections. In this type of networks, uncertainties are almost present, and even the graph topology may not be available, which makes the analysis more complicated. One of the most promising tools to address these problems are graphons, defined as the limits of convergent sequences of dense graphs. In this talk, we will present the fundamentals of graphons and their applications in the estimation of performance indices associated with large networks sampled from graphons. In the first part, we will analyze the stability of a SIS epidemic over a network and its robustness to noise using the properties of the graphon operator. For the second application, we will present a study of the spectrum of the Laplacian matrix of a graph using the degree function of the graphon and the estimation of the well known average effective resistance of sampled networks.

02/11/2021 (14h) [Location: Euler building (room a.002)]
Welcome Seminar

Title: Using photogrammetry for the objective study of ancient bowed instruments: a machine learning approach
Speaker: Philémon Beghin(UCLouvain/INMA)
Abstract: The morphology of today’s violin differs greatly from that of the first instruments of the late 16th century. Indeed, in order to meet the standards suggested by famous orchestras and conservatories, many ancient violins have been recut. It is important for musicologists, violin makers and museum curators to analyse the alterations they have undergone. Specialists agree that the instruments have been reshaped, but have difficulty to prove it rigorously. Moreover, the historical testimonies about this process are imprecise. It is therefore necessary to find an objective way to quantify violin geometry. This project aims to develop a set of algorithmic tools in order to compute an adequate mathematical representation that is able to describe the 3D shape of an object (violin) acquired by photogrammetry. Based on that representation, machine learning techniques will be applied in order to perform clustering and classification with the aim of quantifying their geometric characteristics, their possible anomalies and, if applicable, their original morphology. From an engineering point of view, the development of 3D analyses of objects as complex as violins will allow the growth of methods and knowledge potentially applicable to many fields outside of organology.

Title: Biomechanics of tactile feedback during dexterous manipulation of objects
Speaker: Donatien Doumont(UCLouvain/INMA)
Abstract: The biomechanics of the skin and underlying tissues play a fundamental role in the sense of touch. Indeed, when the finger comes in contact with an object, the deformations induced within these living tissues are translated by the mechanoreceptors (or tactile sensors) into neural signals, which are then interpreted by the brain to generate the appropriate motor response. This project is aimed at better understanding the feedback provided by the tactile afferents during interactions with objects. To that end, we will combine passive stimulation tasks mimicking the mechanical interactions during object manipulation and active manipulation tasks while monitoring the activity of tactile afferents (only in the passive case) and several key biomechanical parameters such as external forces, surface skin deformation, and skin moisture. This combination of techniques will enable us to gain insight into the essential aspects of tactile feedback that enable stable and dexterous control of fingertip forces during manipulation. Such insight will have direct implications for the development of sensorized bionic hands.

Title: Simulation of the stride-to-stride variability of patients with Parkinson’s disease
Speaker: Clémence Vandamme(UCLouvain/INMA)
Abstract:Gait is a complex mechanism involving several neural structures such as the motor cortex, the cerebellum and basal ganglia. It also requires the integration of sensorial feedback from visual, vestibular and peripheral receptors. The complex coordination of these structures is not yet fully understood. In particular, recent studies revealed that gait fluctuations exhibit Long Range Autocorrelation (LRA) such that fluctuations at any given moment are statistically related to those that occur over many different time scales. Up to now, the physiological origin of LRA remains unclear. Moreover, this specific correlation structure is altered in elderly and in people suffering from neurodegenerative diseases, such as Parkinson’s disease. Consequently, it is thought that an optimal level of LRA is a marker of stable gait and high adaptive capabilities. Clinically, LRA indicators could complement the diagnostic of Parkinson's disease and constitutes a precautious marker of risk of fall. This project aims to provide a comprehensive model that includes a continuous-time control of the biomechanics plant for both a healthy population and Parkinson’s patients, as it is an important challenge for fundamental understanding as well as for clinical applications.

Title: Influence of vestibular, visual and somesthesic inputs on dexterous manipulation
Speaker: Simon Vandergooten(UCLouvain/INMA)
Abstract:Since birth we evolve in a steady gravitational environment in which our brain has learned to manipulate objects. For example, we are able to unconsciously optimize the force with which we squeeze objects when handling them. In order to better characterize the influence of gravity on upper limb movement kinematics as well as on the dynamics of prehension (i.e. the act of grasping), several parabolic flight campaigns as well as ground-based experiments were performed. These experiments ultimately led to GRIP, an experiment carried out in the International Space Station that focuses on long-term motor adaptation to microgravity, in particular during dexterous object manipulation. On the ground, our current setup comprising a rotating chair, four motion-tracking cameras and the grip-lift manipulandum allows us to perform control experiments that are necessary for the interpretation of and analysis of GRIP data. With this project, we aim to study how visual, vestibular and somatosensory feedbacks interact and affect the planning of movement trajectory, the perception of the verticality and the anticipative force mechanisms underlying finger-arm coordination.

26/10/2021 (14h) [Location: Euler building (room a.002)]
Welcome Seminar

Title: Employing neural network based control models to understand how brain generates movements
Speaker: Hari Teja Kalidindi (ICTEAM/IoNS)
Abstract:Biological agents display impressive abilities to move under dynamic environmental conditions. Distributed regions in the central nervous system coordinate to generate the motor commands suitable for a given behavioral goal. However, the neural computations that underlie even the simplest of the movements are still equivocal. Historically, one of the main sources of the dispute has been due to the emphasis on describing the motor-encoding in isolated brain regions, by ignoring the effect of key control elements such as sensory-feedback, prediction and the physics of the body under control. In this talk, we demonstrate the utility of mechanistic neural networks as normative models to study neural computations underlying movement control. Particularly, we emulate recent observations from the primate motor cortex - the brain region that is implicated for generating movements.

Title: Sensing of low-rank plus sparse matrices
Speaker: Simon Vary (ICTEAM)
Abstract:Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data. This model is the foundation of robust principle component analysis, and popularized by dynamic-foreground/static-background separation amongst other applications. In this talk we develop guarantees showing that rank-r plus sparsity-s matrices can be recovered by computationally tractable methods from p=O(r(m+n-r)+s)log(mn/s) linear measurements. We establish that the restricted isometry constants for the low-rank plus sparse matrix set remain bounded independent of the problem size provided p/mn, s/p, and r(m+n-r)/p remain fixed. The developed theory and algorithms also apply to the fully observed case of Robust PCA.

19/10/2021 (14h) [Location: Euler building (room a.002)]
David Wozabal (Technical University of Munich)
Multi-Stage Stochastic Programming for AC Optimal Power Flow Problems

Abstract:We propose the first computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in alternating current (AC) power systems. To this end, we use recent results on convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the SDDP algorithm for problems with a Markovian structure employing scenario lattices to discretize the underlying randomness. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal solution of the stochastic AC-OPF problem as long as the SDP relaxations are tight. In the last part of the paper, we set up an extensive case study demonstrating the practical viability of our approach. In particular, we use the IEEE RTS-GMLC network to set up a storage sitting, sizing, and operation problem under uncertainty about demand and renewable generation. We show that the convex SDP relaxation of the stochastic problem is tight except in very rare cases. Furthermore, we demonstrate that after a reasonable number of iterations the algorithm finds a policy with a relatively small SDDP optimality gap that yields a significant added value over rolling deterministic planning.

12/10/2021 (14h) [Location: Euler building (room a.002)]
Vivian De Smedt (PSI Metals Belgium)
Optimization in Steel Industry

Abstract:What are some of the optimization problems of the steel industry? We will discuss the differences between two approaches of the optimization problems: black box vs. expert systems. The size of the solution space being very large some heuristic approaches are needed. We will discuss how to select the heuristics and what are the strong and weak points of the different approaches. The optimization project have to be integrated into workflow that less automatic and have its strong points. We will discuss how to take into account this aspect of the problematic in the conception of the solution

05/10/2021 (14h) [Location: Euler building (room a.002)]
Guillaume Drion (Université de Liège)
Neuromorphic control principles

Abstract:Owing to the recent advances in control engineering and machine learning, and combined with the remarkable improvement of sensors, actuators and computer power, modern high-performance computing systems far surpass human performance in a plethora of complex tasks. However, they consume megawatts of power, are optimized for specific tasks, and are hardly portable. In sharp contrast, biological brains are energy-efficient, are polyvalent, and show impressive adaptive capabilities in uncertain environments. These main differences between brains and current computing architectures are a crucial bottleneck for the expansion of automation in modern society. This situation has led many universities and world-leading companies, which include IBM, Intel, IMEC, or Thales, to investigate novel, brain-inspired computing systems and artificial intelligence technologies, an approach called neuromorphic computing. In this talk, we will approach the design of neuromorphic computing systems from a control engineering approach. We will first study how excitability, a key property of neuronal signaling, can be analyzed and designed following a nonlinear, multiscale feedback approach. Secondly, we will see how such neuromorphic systems can be controlled through loop shaping via a physiological mechanism called neuromodulation. Finally, we will exploit these brain-inspired mechanisms to improve artificial neural network adaptivity and long-term memory on the one hand, and design robust and controllable neuromorphic electronic systems on the other hand

28/9/2021 (14h) [Location: Euler building (room a.002) ]
Josh Taylor (University of Toronto)
Convex Optimization of Bioprocesses

Abstract:In this talk, we begin by optimizing the gradostat, in which several chemostats are interconnected by mass flow and diffusion. The gradostat is of interest both as a classical nonlinear system and because the basic network structure and nonlinearities appear in a wide variety of bioprocesses, including wastewater treatment. We formulate a convex relaxation of the gradostat. The relaxation is exact under several conditions, for instance, if the gradostat is outflow connected and its flow matrix is irreducible. When the microbial growth in the bioreactors is described by the Monod or Contois functions, the relaxation is a second-order cone program, which can be solved at scales of over 10^5 variables in minutes with industrial software. We also discuss how to extend the work to a general class of bioprocesses, and present an example based on wastewater treatment.

21/9/2021 (14h) [Location: Euler building (room a.002) ]
Balázs Gerencser ( Eötvös Loránd University, Hungary)
From theoretical to computable convergence rate of push-sum for consensus

Abstract:We know that reaching average consensus using only local communication along a network is a fundamental building block in the area of distributed computing, leading to applications such as sensor fusion and distributed optimization. We currently analyze schemes based on one such protocol, push-sum, and our target is to understand their convergence speed. We prove a bound on the almost sure convergence rate that is also computable for a class of push-sum algorithms. This extends the works of Iutzeler, Ciblat and Hachem (2013) on similar bounds but in a more restrictive setup and conclusion, and complements the results of Gerencsér and Gerencsér (2019) identifying the exact convergence rate but providing no computable access or approximation