68 citations · 169 across the 22 of their papers we have counts for
23 papers
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
Serge Gratton, Valentin Mercier, Elisa Riccietti +1
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…
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training
S. Gratton, A. Kopanicakova, Ph. L. Toint
A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the mome…
Yet another fast variant of Newton's method for nonconvex optimization
Serge Gratton, Sadok Jerad, Philippe L. Toint
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-dep…
Convergence properties of an Objective-Function-Free Optimization regularization algorithm, including an complexity bound
S. Gratton, S. Jerad, Ph. L. Toint
An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This a…
A coarse space acceleration of deep-DDM
Valentin Mercier, Serge Gratton, Pierre Boudier
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 a…
OPM, a collection of Optimization Problems in Matlab
Serge Gratton, Philippe L. Toint
OPM is a small collection of CUTEst unconstrained and bound-constrained nonlinear optimization problems, which can be used in Matlab for testing optimization algorithms directly (i…
Adaptive Regularization Minimization Algorithms with Non-Smooth Norms and Euclidean Curvature
Serge Gratton, Philippe L. Toint
A regularization algorithm (AR1pGN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularizati…
Latent Space Data Assimilation by using Deep Learning
Mathis Peyron, Anthony Fillion, Selime Gürol +4
Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are availab…
Data Assimilation Networks
Pierre Boudier, Anthony Fillion, Serge Gratton +2
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 thei…
On the iterative solution of systems of the form
Henri Calandra, Serge Gratton, Elisa Riccietti +1
Given a full column rank matrix (), we consider a special class of linear systems of the form with $x, c \in \mathbb{…
Exploiting variable precision in GMRES
Serge Gratton, Ehouarn Simon, David Titley-Peloquin +1
We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm…
On high-order multilevel optimization strategies
Henri Calandra, Serge Gratton, Elisa Riccietti +1
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order…
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method
Henri Calandra, Serge Gratton, Elisa Riccietti +1
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used t…
Minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity
S. Gratton, E. Simon, Ph. L. Toint
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that…
A note on solving nonlinear optimization problems in variable precision
S. Gratton, Ph. L. Toint
This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-p…
Minimizing convex quadratic with variable precision conjugate gradients
S. Gratton, E. Simon, D. Titley-Peloquin +1
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance…
A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis
El houcine Bergou, Youssef Diouane, Serge Gratton
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity a…
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
Serge Gratton, Selime Gürol, Ehouarn Simon +1
The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model a…
On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
S. Gratton, S. Gürol, E. Simon +1
This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its orig…
On the Convergence of a Non-linear Ensemble Kalman Smoother
El houcine Bergou, Serge Gratton, Jan Mandel
Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequenti…
Variational Assimilation for Xenon Dynamical Forecasts in Neutronic using Advanced Background Error Covariance Matrix
Angélique Ponçot, Jean-Philippe Argaud, Bertrand Bouriquet +3
Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of informatio…
4DVAR by ensemble Kalman smoother
Jan Mandel, Elhoucine Bergou, Serge Gratton
We propose to use the ensemble Kalman smoother (EnKS) as linear least squares solver in the Gauss-Newton method for the large nonlinear least squares in incremental 4DVAR. The ense…
A contribution to the conditioning of the total least squares problem
Marc Baboulin, Serge Gratton
We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax=b, we show that this conditio…