Related papers: Gradient flows for bounded linear evolution equati…

In this paper, we introduce a geometric flow for Lagrangian submanifolds in a K\"ahler manifold that stays in its initial Hamiltonian isotopy class and is a gradient flow for volume. The stationary solutions are the Hamiltonian stationary…

We consider singularly perturbed gradient flows in Hilbert spaces, driven by a time-dependent, nonconvex, and nonsmooth energy, and address the convergence of their solutions to curves of critical points of the driving energy functional.…

We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or…

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…

Flavor observables are usually computed with the help of the electroweak Hamiltonian which separates the short-distance from the long-distance regime. The Wilson coefficients are calculated perturbatively, while matrix elements of the…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

We prove an abstract compactness result for gradient flow lines of a non-local unregularized gradient flow equation on a scale Hilbert space. This is the first step towards Floer theory on scale Hilbert spaces.

We consider determining the $\R$-minimizing solution of ill-posed problem $A x = y$ for a bounded linear operator $A: X \to Y$ from a Banach space $X$ to a Hilbert space $Y$, where $\R: X \to (-\infty, \infty]$ is a strongly convex…

We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing…

We prove that the standard gradient flow in parameter space that underlies many training algorithms in deep learning can be continuously deformed into an adapted gradient flow which yields (constrained) Euclidean gradient flow in output…

We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…

Motivated by recent developments in the fields of large deviations for interacting particle system and mean field control, we establish a comparison principle for the Hamilton--Jacobi equation corresponding to linearly controlled gradient…

We show pluriclosed flow preserves the Hermitian-symplectic structures. And we observe that it can actually become a flow of Hermitian-symplectic forms when an extra evolution equation determined by the Bismut-Ricci form is considered.…

We study the asymptotic behaviour of families of gradient flows in a general metric setting, when the metric-dissipation potentials degenerate in the limit to a dissipation with linear growth. We present a general variational definition of…

We present a method for linearising classes of matrix-valued nonlinear partial differential equations with local and nonlocal nonlinearities. Indeed we generalise a linearisation procedure originally developed by P\"oppe based on solving…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

Normalizing flows are a powerful class of generative models demonstrating strong performance in several speech and vision problems. In contrast to other generative models, normalizing flows are latent variable models with tractable…

The gradient expansion is the fundamental organising principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to…

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide…