相关论文: Domain Variations for Moving Boundary Problems
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a…
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…
The analysis and homogenization of a moving boundary problem for a highly heterogeneous, periodic two-phase medium is considered. In this context, the normal velocity governing the motion of the interface separating the two competing phases…
In this paper, we study the existence of strong solutions to the two-phase magnetohydrodynamic equations in a bounded domain $\Omega\subseteq \mathbb{R}^3$. The fluids are incompressible, viscous, and resistive. The surface tension is…
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network and imposes the boundary condition via a Lagrange multiplier,…
As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
Transfer learning under domain shift remains a fundamental challenge due to the divergence between source and target data manifolds. In this paper, we propose MAADA (Manifold-Aware Adversarial Data Augmentation), a novel framework that…
Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the…
We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power $\gamma(x)$ and how it changes. Under a mild continuity assumption on…
An $\mathrm{L}_1$-maximal regularity theory for parabolic evolution equations inspired by the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, the approach yields a framework allowing global-in-time…
Domain adaptation remains a challenge when there is significant manifold discrepancy between source and target domains. Although recent methods leverage manifold-aware adversarial perturbations to perform data augmentation, they often…
We propose an extended framework for marginalized domain adaptation, aimed at addressing unsupervised, supervised and semi-supervised scenarios. We argue that the denoising principle should be extended to explicitly promote domain-invariant…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…