All Years Seminars
2025-03-25 (14h) : Recent trends in Combinatorial Optimization Augmented Machine Learning
At Euler building (room A.002)
Speaker :
Axel Parmentier (Ecole Nationale des Ponts et Chaussées)
Abstract :
Combinatorial optimization augmented machine learning (COAML) is a novel and rapidly growing field that integrates methods from machine learning and operations research to tackle data-driven problems that involve both uncertainty and combinatorics. These problems arise frequently in industrial processes, where firms seek to leverage large and noisy data sets to better optimize their operations. COAML typically involves embedding combinatorial optimization layers into neural networks and training them with decision-aware learning techniques. This talk provides an overview of the field, covering its main applications, algorithms, and theoretical foundations. We will notably emphasize recent contributions on empirical risk minimization and the resulting theoretical guarantees. We also demonstrate the effectiveness of COAML on contextual and dynamic stochastic optimization problems, as evidenced by its winning performance on the 2022 EURO-NeurIPS challenge on dynamic vehicle routing.
2025-03-18 (14h) : Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions
At Euler building (room A.002)
Speaker :
Jing-Rebecca Li (INRIA-ENSTA)
Abstract :
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries.
We present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry.
2025-03-11 (14h) : Optimizing the Present and Future of Smart Electric Power Grids
At Euler building (room A.002)
Speaker :
Miguel Anjos (University of Edinburgh)
Abstract :
A smart grid is the combination of a traditional electrical power system with information and energy both flowing back and forth between suppliers and consumers. This new paradigm introduces major challenges such as the integration of decentralized energy generation, the increase of electric transportation, and the need for electricity consumers to play an active role in the operations of the grid. This presentation will overview the changes in progress in several countries, present some recent research on mathematical optimization models to support these changes, and conclude with a summary of the opportunities for optimization to contribute to the future success of smart grids.
2025-03-04 (14h) : Correctness guarantees for the Burer-Monteiro heuristic on MaxCut-type problems
At Euler building (room A.002)
Speaker :
Irene Waldspurger (Université Paris-Dauphine)
Abstract :
We consider semidefinite optimization problems, that is, where one has to minimize a convex function on the set of semidefinite positive matrices. Sometimes, we know a priori that the solution will be of low rank (for instance, rank 1). This information can be used to make numerical solvers faster. This is the goal of the Burer-Monteiro factorization: we represent the unknown matrix as a product of "thin" matrices (i.e. with few columns); then, we optimize the factors instead of the whole square matrix. Since it reduces the dimensionality of the problem, this method allows for significant speedups. However, it makes the problem non-convex, thereby possibly introducing non-optimal critical points which can cause the solver to fail.
With Faniriana Rakoto Endor, we have considered the specific category of so-called "MaxCut-type" semidefinite problems. We have exhibited a simple property which guarantees that the Burer-Monteiro factorization associated with one of these problems has no non-optimal critical point.
2025-03-03 (14h) : Systematic Design of Control Barrier Function
At Euler building (room A.002)
Speaker :
Marco Nicotra
Abstract :
Control Barrier Functions (CBFs) have become an increasingly popular tool for constrained control due to their simplicity and performance. Despite promising results in many applications, the widespread adoption of CBFs has been limited by the absence of a systematic method for designing CBFs for nonlinear systems with arbitrary state and input constraints.
This talk will provide a brief overview of CBFs and show the dangers of using improper CBFs to enforce constraints. Then, it will draw parallels between CBFs and a different Safety Filter framework known as Reference Governors (RGs). Using existing tools from the RG literature, the talk will introduce a simple and systematic approach for CBF design.
Seminars
INMA Contact Info
Mathematical Engineering (INMA)
L4.05.01
Avenue Georges Lemaître, 4
+32 10 47 80 36
secretaire-inma@uclouvain.be
Mon – Fri 9:00A.M. – 5:00P.M.
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