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Robust Ultrasound Travel-time Tomography Using the Bent Ray Model
Publications associées (50)
Residual-based attention in physics-informed neural networks
Nikolaos Stergiopoulos, Sokratis Anagnostopoulos
Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...
Lausanne2024A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
Alexandre Caboussat, Dimitrios Gourzoulidis
We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...
SPRINGER/PLENUM PUBLISHERS2022Last iterate convergence of SGD for Least-Squares in the Interpolation regime
Nicolas Henri Bernard Flammarion, Aditya Vardhan Varre, Loucas Pillaud-Vivien
Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...
2021STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization
In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...
2021On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method
The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...
Springer-Verlag2021Data-Driven Convergence Prediction of Astrobots Swarms
Denis Gillet, Jean-Paul Richard Kneib, Matin Macktoobian, Francesco Basciani
Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...
2021Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates
Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, ...
MICROTOME PUBLISHING2021On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems
Volkan Cevher, Ali Kavis, Shaul Nadav Hallak
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...
2020Adaptive Gradient Descent without Descent
We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...
2020MATHICSE Technical Report : A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters
Fabio Nobile, Matthieu Claude Martin, Panagiotis Tsilifis
In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form of PDEs with rand ...
MATHICSE2020