相关论文: Compositional maps for registration in complex geo…

This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…

We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

The central problem of strip theory is the calculation of potential flowaround 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential…

Nonlinear registration of 2D histological sections with corresponding slices of MRI data is a critical step of 3D histology reconstruction. This task is difficult due to the large differences in image contrast and resolution, as well as the…

This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investigate three canonical classes of models: nonlinear impedance,…

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…

Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…

We present a general approach for the treatment of parameterized geometries in projection-based model order reduction. During the offline stage, given (i) a family of parameterized domains $\{ \Omega_{\mu}: \mu \in \mathcal{P} \} \subset…

We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…

We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…

We present HyperMorph, a learning-based strategy for deformable image registration that removes the need to tune important registration hyperparameters during training. Classical registration methods solve an optimization problem to find a…

We consider a \emph{family} $(P_\omega)_{\omega \in \Omega}$ of elliptic second order differential operators on a domain $U_0 \subset \mathbb{R}^m$ whose coefficients depend on the space variable $x \in U_0$ and on $\omega \in \Omega,$ a…

Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two point clouds. However, the finding of reliable correspondence relies on establishing a robust and…

In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

In this paper, we consider the problem of solving the $\partial \bar{\partial}$ with prescribed support for forms or currents in a domain $\Omega$ of an complex manifold $X$.

We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of…

We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…