Related papers: A New Functional for Variational Mesh Generation a…
Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change…
In this paper, we present a feature-aware SPH method for the concurrent and automated isotropic unstructured mesh generation. Two additional objectives are achieved with the proposed method compared to the original SPH-based mesh generator…
The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
Learning a distribution conditional on a set of discrete-valued features is a commonly encountered task. This becomes more challenging with a high-dimensional feature set when there is the possibility of interaction between the features. In…
We present a novel framework for variable selection in Fr\'echet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices.…
Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
Generating novel and functional protein sequences is critical to a wide range of applications in biology. Recent advancements in conditional diffusion models have shown impressive empirical performance in protein generation tasks. However,…
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured…
We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
In this paper, a novel model of 3D elastic mesh is presented for image segmentation. The model is inspired by stress and strain in physical elastic objects, while the repulsive force and elastic force in the model are defined slightly…