Related papers: Spherical Authalic Energy Minimization for Area-Pr…

This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…

Targeting solutions over `flat' regions of the loss landscape, sharpness-aware minimization (SAM) has emerged as a powerful tool to improve generalizability of deep neural network based learning. While several SAM variants have been…

We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

Many genus-0 surface mapping tasks such as landmark alignment, feature matching, and image-driven registration, can be reduced (via an initial spherical conformal map) to optimizing a spherical self-homeomorphism with controlled distortion.…

In the present work, genetic algorithm method (GA) is applied to the problem of impurity at the center of a spherical quantum dot for infinite confining potential case. For this purpose, any trial variational wave function is considered for…

Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…

This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…

These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…

Sparse autoencoders (SAEs) are used to disentangle the dense, polysemantic internal representations of large language models (LLMs) into interpretable, monosemantic concepts. However, standard $\ell_1$-regularized SAEs suffer from feature…

Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…

Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…

We propose a structure-preserving parametric finite element method (SP-PFEM) for discretizing the surface diffusion of a closed curve in two dimensions (2D) or surface in three dimensions (3D). Here the "structure-preserving" refers to…

Energy efficiency (EE) is an important aspect of satellite communications. Different with the existing algorithms that typically use the first-order Taylor lower bound approximation to convert non-convex EE maximization (EEM) problems into…

Deep neural networks often suffer from poor generalization due to complex and non-convex loss landscapes. Sharpness-Aware Minimization (SAM) is a popular solution that smooths the loss landscape by minimizing the maximized change of…

The problem of small area estimation (SAE) is how to produce reliable estimates of characteristics of interest such as means, counts, quantiles, etc., for areas or domains for which only small samples or no samples are available, and how to…

The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…

Conventional image compression methods typically aim at pixel-level consistency while ignoring the performance of downstream AI tasks.To solve this problem, this paper proposes a Semantic-Assisted Image Compression method (SAIC), which can…

We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…

Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…