Related papers: Shape flows for spectral optimization problems
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…
We carry on our study of the connection between two shape optimization problems with spectral cost. On the one hand, we consider the optimal design problem for the survival threshold of a population living in a heterogenous habitat…
The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of this model from the literature and give a new formulation…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
Novel techniques in evolutionary optimization, simulation and machine learning allow for a broad analysis of domains like fluid dynamics, in which computation is expensive and flow behavior is complex. Under the term of full domain analysis…
Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla…
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…
We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency…
The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the…
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…
We propose a generalization of the gradient flow equation for quantum field theories with nonlinearly realized symmetry. Applying the equation to $\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in four dimensions, we construct a…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…