Related papers: Discrete Total Variation Flows Without Regularizat…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The introduced model is based on same design principles as Condat's…
In this paper, a regularity result for the Willmore flow is presented. It is established by means of a truncated translation technique in conjunction with the Implicit Function Theorem.
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
The partial stochastic realization of periodic processes from finite covariance data has recently been solved by Lindquist and Picci based on convex optimization of a generalized entropy functional. The meaning and the role of this…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
We present a proof-of-principle implementation of the first fully covariant filtering scheme applied to relativistic fluid turbulence. The filtering is performed with respect to special observers, identified dynamically as moving with the…
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We prove universality of a macroscopic behavior of solutions of a large class of semi-linear parabolic SPDEs on $\mathbb{R}_+\times\mathbb{T}$ with fractional Laplacian $(-\Delta)^{\sigma/2}$, additive noise and polynomial non-linearity,…
In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and…
A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…