Saddle-to-saddle dynamics in diagonal linear networks
S Pesme, N Flammarion - Advances in Neural Information …, 2023 - proceedings.neurips.cc
In this paper we fully describe the trajectory of gradient flow over $2 $-layer diagonal linear
networks for the regression setting in the limit of vanishing initialisation. We show that the …
networks for the regression setting in the limit of vanishing initialisation. We show that the …
Rate-independent systems
A Mielke, T Roubíček - Applied Mathematical Sciences, 2015 - Springer
Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …
material models for shape-memory alloys that are flexible enough to encompass nonlinear …
On Evolutionary -Convergence for Gradient Systems
A Mielke - Macroscopic and large scale phenomena: coarse …, 2016 - Springer
In these notes we discuss general approaches for rigorously deriving limits of generalized
gradient flows. Our point of view is that a generalized gradient system is defined in terms of …
gradient flows. Our point of view is that a generalized gradient system is defined in terms of …
A vanishing viscosity approach to a rate-independent damage model
D Knees, R Rossi, C Zanini - Mathematical Models and Methods in …, 2013 - World Scientific
We analyze a rate-independent model for damage evolution in elastic bodies. The central
quantities are a stored energy functional and a dissipation functional, which is assumed to …
quantities are a stored energy functional and a dissipation functional, which is assumed to …
BV solutions and viscosity approximations of rate-independent systems∗
In the nonconvex case, solutions of rate-independent systems may develop jumps as a
function of time. To model such jumps, we adopt the philosophy that rate-independence …
function of time. To model such jumps, we adopt the philosophy that rate-independence …
Nonsmooth analysis of doubly nonlinear evolution equations
In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in
Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general …
Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general …
On the inviscid limit of a model for crack propagation
D Knees, A Mielke, C Zanini - Mathematical Models and Methods in …, 2008 - World Scientific
We study the evolution of a single crack in an elastic body and assume that the crack path is
known in advance. The motion of the crack tip is modeled as a rate-independent process on …
known in advance. The motion of the crack tip is modeled as a rate-independent process on …
[HTML][HTML] Cosh gradient systems and tilting
MA Peletier, A Schlichting - Nonlinear Analysis, 2023 - Elsevier
We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …
We show how such dissipation potentials emerge in large deviations of jump processes …
Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems
Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-
independent flows by adding a superlinear vanishing-viscosity dissipation. We address the …
independent flows by adding a superlinear vanishing-viscosity dissipation. We address the …
Differential, energetic, and metric formulations for rate-independent processes
In these notes we want to give an overview of the recently developed theory for rate-
independent systems. Such systems are used to model hysteresis, dry friction …
independent systems. Such systems are used to model hysteresis, dry friction …