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Directed mean curvature flow in noisy environment
Publications associées (32)
The Allen-Cahn equation with generic initial datum
We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets o ...
SPRINGER HEIDELBERG2023An Accelerated First-Order Method for Non-convex Optimization on Manifolds
Nicolas Boumal, Christopher Arnold Criscitiello
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...
SPRINGER2022Robustness via curvature regularization, and vice versa
Pascal Frossard, Seyed Mohsen Moosavi Dezfooli, Alhussein Fawzi
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the ...
IEEE2019A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities
The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...
EPFL2019Robustness via curvature regularization, and vice versa
Pascal Frossard, Seyed Mohsen Moosavi Dezfooli, Alhussein Fawzi
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the ...
2018Out-of-plane instability of thin reinforced concrete walls under seismic loading
Out of plane instability of reinforced concrete walls is a failure mechanism observed rather recently following the earthquakes in Chile (2010) and New Zealand (2011). Global out of plane instability is a phenomenon that may occur in thin walls, subjected ...
EPFL2018Gaussian Curvature as an Identifier of Shell Rigidity
In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. ...
Springer Verlag2017Axially equilibrated displacement-based beam element for simulating the cyclic inelastic behaviour of RC members
Katrin Beyer, João Saraiva Esteves Pacheco de Almeida, Danilo Tarquini
Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits since they directly relate to damage and are the ...
Wiley-Blackwell2017A vector field method on the distorted Fourier side and decay for wave equations with potentials
Joachim Krieger, Roland Donninger
We study the Cauchy problem for the one-dimensional wave equation \[ \partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0. \] The potential is assumed to be smooth with asymptotic behavior \[ V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty. \] ...
2016Isogeometric Analysis of geometric partial differential equations
Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi
We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...
Elsevier2016