Serge Gratton
YOU?
Author Swipe
Multilevel Monte Carlo methods for ensemble variational data assimilation Open
Ensemble variational data assimilation relies on ensembles of forecasts to estimate the background error covariance matrix B. The ensemble can be provided by an ensemble of data assimilations (EDA), which runs independent perturbed data as…
Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes Open
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the regu…
Feature Representation Transferring to Lightweight Models via Perception Coherence Open
In this paper, we propose a method for transferring feature representation to lightweight student models from larger teacher models. We mathematically define a new notion called \textit{perception coherence}. Based on this notion, we propo…
Convolutional Rectangular Attention Module Open
In this paper, we introduce a novel spatial attention module that can be easily integrated to any convolutional network. This module guides the model to pay attention to the most discriminative part of an image. This enables the model to a…
A FILTERED MULTILEVEL MONTE CARLO METHOD FOR ESTIMATING THE EXPECTATION OF CELL-CENTERED DISCRETIZED RANDOM FIELDS Open
In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators h…
Deterministic and probabilistic rounding error analysis of neural networks in floating-point arithmetic Open
International audience
Multilevel Monte Carlo methods for ensemble variational data assimilation Open
Ensemble variational data assimilation relies on ensembles of forecasts to estimate the background error covariance matrix B. The ensemble can be provided by an Ensemble of Data Assimilations (EDA), which runs independent perturbed data as…
View article: Two-level deep domain decomposition method
Two-level deep domain decomposition method Open
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network …
Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is $o(ε^{-2})$ rather than $\mathcal{O}(ε^{-2})$ Open
We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of…
Deterministic and probabilistic backward error analysis of neural networks in floating-point arithmetic Open
The use of artificial neural networks is now becoming widespread across a wide variety of tasks. In this context of very rapid development, issues related to the storage and computational performance of these models emerge, since networks …
A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity Open
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(ε^{-3/2})$ complexity bound f…
Complexity of Adagrad and other first-order methods for nonconvex optimization problems with bounds constraints Open
A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad …
Training More Robust Classification Model via Discriminative Loss and Gaussian Noise Injection Open
Robustness of deep neural networks to input noise remains a critical challenge, as naive noise injection often degrades accuracy on clean (uncorrupted) data. We propose a novel training framework that addresses this trade-off through two c…
CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle System Open
In Vapor Cycle Systems, the mass flow sensor playsa key role for different monitoring and control purposes. However,physical sensors can be inaccurate, heavy, cumbersome, expensive orhighly sensitive to vibrations, which is especially prob…
Combining Statistical Depth and Fermat Distance for Uncertainty Quantification Open
We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to …
A Review of Fault Diagnosis Techniques Applied to Aircraft Air Data Sensors Open
Air data sensors provide essential measurements to ensure the availability of autopilot and to maintain aircraft performance, flight envelope protection and optimal aerodynamic surfaces control laws. The importance of these sensors imply t…
An optimally fast objective-function-free minimization algorithm using random subspaces Open
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this ran…
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training Open
International audience
An adaptive regularization method in Banach spaces Open
International audience
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks Open
Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level met…
Data Assimilation Networks Open
Data Assimilation aims at estimating the posterior conditional probability density functions based on error statistics of the noisy observations and the dynamical system. State of the art methods are sub‐optimal due to the common use of Ga…
Yet another fast variant of Newton's method for nonconvex optimization Open
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is regul…
Neural prediction model for transition onset of a boundary layer in presence of two-dimensional surface defects Open
Predicting the laminar to turbulent transition is an important aspect of computational fluid dynamics because of its impact on skin friction. Traditional transition prediction methods such as local stability theory or the parabolized stabi…
Data Assimilation Networks Open
Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the …
Adversarial attacks via Sequential Quadratic Programming Open
Deep neural networks (DNN) achieve state-of-the-art performance in many machine learning tasks and in various types of applications. Their efficiency in solving complex problems has led to apply deep learning techniques in safety-critical …
Neural Prediction Model for Transition Onset of a Boundary-Layer in Presence of 2D Surface Defects (ODAS 2022) Open
International audience
Multilevel Monte Carlo estimation of background error covariances in ensemble variational data assimilation Open
In ensemble variational (EnVar) data assimilation systems, background error covariances are sampled from an ensemble of forecasts evolving with time. One possible way of generating this ensemble is by running an Ensemble of Data Assimilati…
Neural Prediction Model for Transition Onset of a Boundary-Layer in Presence of 2D Surface Defects Open
International audience
A coarse space acceleration of deep-DDM Open
The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the …
Latent space data assimilation by using deep learning Open
Performing data assimilation (DA) at low cost is of prime concern in Earth system modeling, particularly in the era of Big Data, where huge quantities of observations are available. Capitalizing on the ability of neural network techniques …