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The flexible boundary condition method (FBCM) is a well-established method for the efficient study of complex non-linear atomistic defects while avoiding finite-size effects. The method uses lattice Green's functions (LGFs) to effectively embed an atomisti ...
This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...
We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a soluti ...
Data augmentation is a widely adopted technique for avoiding overfitting when training deep neural networks. However, this approach requires domain-specific knowledge and is often limited to a fixed set of hard-coded transformations. Recently, several work ...
The objective of this thesis is to provide a mathematical and computational framework for the proactive maintenance of complex systems with a particular application to structural health monitoring (SHM). SHM techniques rely primarily on sensor responses to ...
For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. We propose an approach based on log barriers to find a local solution of a non-convex non-smooth ...
The aim of this master project is to develop a fast computing method for the analysis of structures with non-linear geometric behavior. The Dynamic Relaxation (DR) method is employed instead of the better known Newton-Raphson iteration process based on Fin ...
This paper presents neural network regression models for predicting the nonlinear static and linearized dynamic reaction forces of spiral grooved gas journal bearings. The partial differential equations (PDEs) are sampled, based on a full factorial and ran ...
Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U (1) model at the Wilson-Fisher fixed point in D = 4 - epsilon can be computed semiclassically for arbitrary values of lambda n, where lambda is the pertu ...