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Concept

Calcul des variations

Publications associées (31)

Integral Convexity And Parabolic Systems

Bernard Dacorogna

In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...

SIAM PUBLICATIONS2020

Adaptive 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 ...

2020

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Michaël Unser, Shayan Aziznejad, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

2020

A gyrokinetic model for the plasma periphery of tokamak devices

Paolo Ricci, Paolo De Los Rios, Rogério Manuel Cabete De Jesus Jorge, Baptiste Jimmy Frei

A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the a ...

Cambridge University Press2020

A note on efficient computation of privileged directions in modifier adaptation

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti, Martand Singhal

In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially pe ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates

Luigi Forcella

We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...

2021

Quantum Monte Carlo approach to the non-equilibrium steady state of open quantum systems

Alexandra Nagy

Many-body open quantum systems are exposed to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. As the exact treatment of such models is generally unfeasible, it is favourable to formulate an approximate descri ...

EPFL2020

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Lenka Zdeborová, Florent Gérard Krzakala

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

Explicit dynamic approach for unbounded domains in frictional contact with Rate and State laws

Jean-François Molinari, Roozbeh Rezakhani

The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed ...

ELSEVIER2020

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Shaul Nadav Hallak

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...

SPRINGER/PLENUM PUBLISHERS2020