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SUMMARY:Séminaire des doctorant·es SO
DTSTART:20260616T091500Z
DTEND:20260616T101500Z
DTSTAMP:20260614T035600Z
UID:indico-event-14486@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexey Lazarev (IMT\, ANITI)\, Daphné Matoses (UT\,
  IMT\, INSERM\, IRESP)\, Naomi Albukerque (IMT\, Laplace)\, Younes Essafou
 ri (IMT\, CNRS)\, Margot Ferré (ENAC\, IMT)\n\nAlexey Lazarev (IMT\, ANIT
 I)\nGeometry of latent spaces: curvature regularization and Riemannian clu
 steringTwo geometric contributions for autoencoder latent spaces are prese
 nted. The first is a curvature regularization framework that augments the 
 autoencoder loss with curvature-based penalties and auxiliary regularizers
  to promote structured and interpretable latent representations. The secon
 d is a Riemannian k-means algorithm that leverages geodesic approximations
  derived from a Faber–Schauder basis. Together\, these approaches incorp
 orate geometric information into both representation learning and clusteri
 ng\, enabling a deeper understanding and exploitation of latent-space stru
 cture.\n\nNaomi Albukerque (IMT\, Laplace)\nPhysics-Informed Learning for 
 Charge Transport Characterization in Dielectric MaterialsElectrical transp
 ort and space charge accumulation in insulating materials play a key role 
 in the performance and reliability of high-voltage electrical systems. Cha
 racterizing the transport mechanisms within a material from experimental o
 bservations remains a challenging inverse problem. This work addresses the
  inverse problem of identifying the parameters of a PDE-based charge trans
 port model from experimental measurements. The proposed approach combines 
 regularized deconvolution techniques and Physics-Informed Neural Networks 
 (PINNs) to exploit both measurement data and prior physical knowledge. Cha
 rge density profiles are first reconstructed from indirect observations ob
 tained through the Pulsed Electro-Acoustic (PEA) method. These profiles ar
 e then used to train a PINN that embeds the governing partial differential
  equations into the learning process\, enabling the simultaneous estimatio
 n of state variables and unknown model parameters. Finally\, a global sens
 itivity analysis will be performed to quantify the influence of the identi
 fied parameters on the model outputs.\n\nDaphné Matoses (UT\, IMT\, INSER
 M\, IRESP)\nCausal inference and synthetic patients in randomized trialsRa
 ndomized Controlled Trials (RCTs) are the gold standard for causal inferen
 ce\, but they suffer from small sample sizes\, high costs\, and ethical co
 nstraints. To estimate the Average Treatment Effect (ATE)\, several estima
 tors are available\, from simple difference-in-means to doubly robust meth
 ods such as AIPW\, all relying on standard identification assumptions. A n
 atural idea is to supplement the trial with synthetic data to improve thes
 e estimations. We show that endogenous synthetic data\, generated from the
  trial itself\, bring no additional Fisher information about the ATE. Exog
 enous synthetic data can help\, but only if the generative model is accura
 te enough\, which raises the question of what makes a good generator.\n\nM
 argot Ferré (ENAC\, IMT)\nStochastic Mirror Descent & Application to the 
 estimation of Sobol' indicesSobol' indices are widely used in Global Sensi
 tivity Analysis to quantify the sensitivity of a random model with respect
  to its input variables. Classical estimators\, such as the Pick-Freeze es
 timator\, are asymptotically efficient but estimate only one index at a ti
 me. This poster presents how Stochastic Mirror Descent (SMD) algorithms en
 able the simultaneous estimation of all Sobol' indices. We establish gener
 al convergence results for SMD under strong convexity assumptions\, and di
 scuss the work of Gadat\, Costa\, Gendre and Klein (2025)\, which formulat
 es Sobol' index estimation as a constrained optimization problem solved th
 rough a constrained SMD algorithm. Basedon negative entropy\, this scheme 
 yields an explicit estimator with almost sure convergence guarantees. Futu
 re work focuses on deriving Central Limit Theorems for general SMD estimat
 ors.\n\nYounes Essafouri (IMT\, CNRS)\nA Framework for Explainable AI in W
 eather Forecasting: Diagnosing Deep Learning Models via Gradient-Based Att
 ributionsEach day\, potentially critical decisions made by governments and
  organizations depend on accurate weather forecasts\, from deciding whethe
 r to evacuate ahead of a storm to simply carrying an umbrella. In this con
 text\, Deep Learning (DL) models are emerging as a popular and  computati
 onally efficient alternative to traditional Numerical Weather Prediction (
 NWP) models\, offering the potential to capture complex data patterns that
  explicit physical equations may miss (lam2023). However\, their opaque (b
 lack-box) nature remains a barrier to operational trust. Explainable AI (X
 AI) seeks to address this opacity by revealing the decision process behind
  predictions. Indeed\, classical XAI techniques can expose when DL models 
 rely on spurious corrélations rather than causal physical mechanisms (gei
 rhos2020). Yet their direct application to meteorological data often produ
 ces attribution maps that are noisy (kim2019) and difficult to interpret d
 ue to their high dimensionality. It also remains unclear whether these too
 ls can consistently identify the complex physical drivers inherent in NWP 
 (bommer2024).Building on previous work (bommer2024\, kim2023\, yang2024)\,
  we establish a framework to generate compact and interpretable explanatio
 ns of local weather forecast predictions produced by deep neural networks.
  These explanations build on the output of gradient-based methods such as 
 VanillaGrad and SmoothGrad (smilkov2017)\, which scale well to high-dimens
 ional data. More specifically\, our framework enables targeted analysis by
  selecting a region of interest (e.g.\, the Paris area) and a target varia
 ble (e.g.\, accumulated precipitation). It therefore answers the question:
  “Why did the neural network predict this feature at this location?” T
 o do so\, it first computes dense attribution maps with respect to all inp
 ut variables (e.g.\, wind components at varying altitudes). Traditionally\
 , bounding boxes are used to define the region of importance in these maps
  (kim2023)\, but they cannot convey detailed directional information. We t
 herefore propose determining régions of importance using “confidence el
 lipses” that summarize the center\, principal directions\, and importanc
 e of the most concentrated regions. Unlike bounding boxes\, these ellipses
  displayed over the raw attribution maps as a background\, provide rich an
 d easily interpretable information about the directionality and spatial sp
 read of the model’s focus.Preliminary results on the hybrid transformer-
 convolutional model UNETR++ (shaker2024)\, trained and tested on the TITAN
  dataset from Météo-France (comprising hourly surface and vertical profi
 les of wind\, temperature\, and geopotential over metropolitan France)\, d
 emonstrate our framework’s relevance for explaining predictions from dee
 p neural networks. We were able to verify that different trained models su
 ccessfully capture the vertical hierarchy of atmospheric variables\, evide
 nced by an effective receptive field that expands with increasing altitude
 . More interestingly\, our framework allowed us to identify systematic bia
 ses learned during training that correlate with known physical phenomena. 
 These findings serve as a foundational step toward future work on developi
 ng novel explainability methods to detect whether trained models capture c
 omplex physical mechanisms.\n\nhttps://indico.math.cnrs.fr/event/14486/
LOCATION:Salle K. Johnson (1R3\, 1er étage)
URL:https://indico.math.cnrs.fr/event/14486/
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