All Years Seminars
[INMA] 2025-02-25 (14h) : Noise modelling and analysis of nonlinear circuits and systems: From statistical mechanics to nonlinear dynamics
At Maxwell building (Shannon room)
Speaker :
Michele Bonnin (Polytechnico di Torino)
Abstract :
The theory of random fluctuations in linear systems does not extend to the internal noise in nonlinear systems. In this talk, we will review the standard methods for modeling internal noise in linear circuits and systems. After examining the thermodynamic requirements for a consistent model, it will be demonstrated that applying linear-system methods to nonlinear systems leads to circuit behaviors that violate thermodynamic principles. A series of tests will be introduced to assess whether a given noise model for nonlinear devices aligns with accepted thermodynamic principles. We will explore the validity of Gaussian and shot-noise models for nonlinear devices, as well as the limitations and shortcomings of approaches based on Langevin and Fokker-Planck equations. Additionally, a stochastic description using the master equation will be presented, which relates to the one-time probability density of Markov processes governing the fluctuating electrical quantities. Finally, we will discuss the implications of these findings for emerging computational paradigms such as neuromorphic and reservoir computing.
[INMA] 2025-02-18 (14h) : Deep Learning Mass Mapping with Conformal Predictions
At Euler building (room A.002)
Speaker :
Hubert Leterme (Ensicaen, CEA Paris-Saclay)
Abstract :
In this talk, I will introduce a plug-and-play (PnP) approach for mapping the distribution of dark matter in the sky using weak gravitational lensing and noisy shear measurements. This method aims to deliver accurate and efficient mass estimates without the need to retrain deep learning models for each new galaxy survey or sky region. Instead, a single model is trained on simulated convergence maps with Gaussian white noise corruption. To enhance reliability, we incorporate a distribution-free uncertainty quantification (UQ) method, conformalized quantile regression (CQR), into the mass mapping framework. Leveraging a simulation-derived calibration set, CQR provides rigorous coverage guarantees, independent of any specific prior data distribution. We benchmark this PnP approach against existing mass mapping methods, including Kaiser-Squires, Wiener filtering, MCALens, and DeepMass. Our results demonstrate that while miscoverage rates, after calibration with CQR, remain consistent across methods, the choice of mass mapping technique significantly impacts the size of the resulting error bars.
[INMA] 2025-02-11 (14h) : Climate science : a goldmine for applied mathematicians
At Euler building (room A.002)
Speaker :
Francois Massonnet (UCLouvain - PHYS/ELIC)
Abstract :
Climate science presents a wealth of mathematical challenges, many of which are unknown to the applied mathematics community. From linear feedback theory to nonlinear dynamical systems, from optimization in decision-making to inverse problems in detection and attribution, applied mathematics is fundamental to our understanding of the climate system. Numerical methods form the backbone of climate models, while machine learning is transforming predictions, weather regime classification, and the tracking of extreme events such as hurricanes and ocean eddies. In this talk, I will present concrete examples where applied mathematics plays a crucial role in climate science, highlighting opportunities for deeper collaboration between our institutes. Everyone is welcome!
[INMA] 2025-02-04 (14h) : Newcomers seminars (PhDs)
At Euler building (room a.002)
Section 1:Large Language Models for Safety-Critical Control
Speaker :
Amir Bayat (PhD UCLouvain/INMA)
Abstract : Large Language Models (LLMs) have demonstrated remarkable capabilities in recent years. Their proficiency in tasks such as question answering, text summarization, and code generation has revolutionized various fields, including education, healthcare, and more. LLMs are user-friendly, offering intuitive interfaces that make interaction seamless. However, despite these strengths, they fall short in engineering applications like robotic task planning and execution. In their current state, LLMs are neither reliable nor safe for performing such actions.
On the other hand, symbolic control, also known as abstraction-based control, is a powerful method for managing complex cyber-physical systems. This approach involves designing a controller for an abstracted version of the system and then refining it to control the original system. While effective, this method requires formal language specifications, which demand significant training and expertise to create.
Our long-term goal is to integrate the strengths of both LLMs and symbolic control for cyber-physical systems. By leveraging the user-friendly interaction capabilities of LLMs alongside the safety and reliability of symbolic control, we aim to develop systems that ensure both usability and robustness
Section 2:Data-driven Event-triggered Control for Discrete-time LTI Systems
Speaker :
Vijayanand Digge (PhD UCLouvain/INMA)
Abstract : Inspired by recent work on data-driven control, this work presents data-driven event-triggered control strategies for discrete-time linear time-invariant (LTI) systems. The results presented do not require explicit identification of the system parameters and are based on the input and state data collected from the system during an open-loop experiment. The design of event-triggered control consists of two stages: finding a state feedback controller that exponentially stabilizes the system and designing an event-triggered policy that determines the instances at which the control law needs to be updated. The proposed designs in both stages involve solving semi-definite programs with data-dependent linear matrix inequalities (LMIs) as constraints. For the event-triggered implementation, we employ a relative thresholding mechanism, and the range of the thresholding parameter is derived using S-procedure. Further, conditions on the thresholding parameter are derived that ensure both pre-specified exponential convergence and non-trivial event-triggering.
Section 3:Impact of Fibre Assignments on Fourier Space Galaxy Clustering Statistics
Speaker :
Jana Jovcheva (PhD UCLouvain/INMA)
Abstract : Due to instrumental limitations, spectroscopic redshift surveys cannot measure the redshifts for all targets. The physical size of the spectroscopic fibres sets a limit on the angular separation between two galaxies at which their redshifts can be measured simultaneously, known as the fibre collision scale. Fibre allocation algorithms attempt to maximise the number of observed targets and minimise the effects of collisions, but it remains impossible to efficiently measure the redshift of every target. The resulting incompleteness in the data biases galaxy clustering statistics such as the power spectrum and bispectrum, which can prevent robust inference of cosmological parameters. I quantify the impact of fibre assignments on the power spectrum and bispectrum for the Dark Energy Spectroscopic Instrument (DESI) first generation mock catalogues, assess the effectiveness of a simple nearest neighbour correction at recovering the true statistics, and consider two alternative schemes to improve the accuracy of clustering measurements. This analysis provides insights for mitigating fibre collision effects and enhancing the cosmological utility of DESI data and future surveys.
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[INMA] 2024-12-03 (14h) : MadNLP: a GPU-ready interior-point solver
At Euler building (room A.002)
Speaker :
François Pacaud ((Mines Paris - PSL))
Abstract :
The interior-point method (IPM) has become a standard algorithm to solve large-scale optimization problems. Traditionally, IPM solves a sequence of symmetric indefinite linear systems, or Karush-Kuhn-Tucker (KKT) systems, that are increasingly ill-conditioned as we approach the solution. As such, solving a KKT system with traditional sparse factorization methods requires numerical pivoting, making parallelization difficult. We present two novel interior-point methods that circumvent this issue. The first method intervenes at the level of the linear algebra: it condenses IPM's KKT system into a symmetric positive-definite matrix and solve it with a Cholesky factorization, stable without pivoting. Although condensed KKT systems are more prone to ill-conditioning than the original ones, they exhibit structured ill-conditioning that mitigates the loss of accuracy. The second method mixes IPM with an Augmented Lagrangian method (Auglag-IPM). The Augmented Lagrangian term adds an implicit dual regularization to the problem; as a result the KKT systems write as symmetric quasi-definite (SQD) matrices, also factorizable without pivoting. Aside, the Auglag-IPM is able to solve degenerate optimization problems, in particular nonlinear programs with complementarity constraints. Both methods have been implemented on the GPU using MadNLP.jl, an optimization solver interfaced with the NVIDIA sparse linear solver cuDSS and with the GPU-accelerated modeler ExaModels.jl. Our experiments on large-scale OPF instances reveal that GPUs can attain up to a tenfold speed increase compared to CPUs. In addition, Auglag-IPM is able to solve complicated optimization problems that are not solvable by a classical IPM algorithm.
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