Related papers: Shape flows for spectral optimization problems
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems.…
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…
We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometric flows have been used frequently in axisymmetric settings,…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…
Normalizing flows are a powerful tool to create flexible probability distributions with a wide range of potential applications in cosmology. Here we are studying normalizing flows which represent cosmological observables at field level,…
We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…
Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'function composition' approach involving local shape derivatives…
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…
Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of…
We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…
We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…
We formulate gradient flow dynamics generated by two natural actions of the quantum metric for an isolated set of Bloch bands. Specializing to two spatial dimensions, we derive Bogomolny-type lower bounds that relate these actions to the…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed…