https://neckpinch.com/authors/kerrek-stinson/New arXiv papers by Kerrek Stinson, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2412.02567arxiv:2412.02567Tue, 03 Dec 2024 00:00:00 GMTLikhit Ganedi, Alice Marveggio, Kerrek Stinson — We consider a variational model for heterogeneous phase separation, based on a diffuse interface energy with moving wells. Our main result identifies the asymptotic behavior of the first variation of the phase field energies as the width of the diffuse interface vanishes. This convergence result allows us to deduce a Gibbs-Thomson relation for heterogeneous surface tensions. Proceeding from this information, we prove that (weak) solutions of the Allen-Cahn equation with space dependent potential converge to a BV solution of weighted mean curvature flow, under an energy convergence hypothesis. Additionally, relying on the relative energy technique, we establish a weak-strong uniqueness principle for solutions of weighted mean curvature flow.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2404.14402arxiv:2404.14402Mon, 22 Apr 2024 00:00:00 GMTLeon Bungert, Tim Laux, Kerrek Stinson — We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as a regularization problem, we introduce a modified training scheme that constitutes a minimizing movements scheme for a nonlocal perimeter functional. We prove that the scheme is monotone and consistent as the adversarial budget vanishes and the perimeter localizes, and as a consequence we rigorously show that the scheme approximates a weighted mean curvature flow. This highlights that the efficacy of adversarial training may be due to locally minimizing the length of the decision boundary. In our analysis, we introduce a variety of tools for working with the subdifferential of a supremal-type nonlocal total variation and its regularity properties.Mean curvature flowAnisotropic & nonlocal flowsWeak & singular flows https://arxiv.org/abs/2212.11939arxiv:2212.11939Thu, 22 Dec 2022 00:00:00 GMTTim Laux, Kerrek Stinson, Clemens Ullrich — The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models, and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak-strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals.Mean curvature flowAnisotropic & nonlocal flowsWeak & singular flowsStability & uniquenessPhase fields & multiphase flows