Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Hong, Qingguo"'
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by parameterizing a set
Externí odkaz:
http://arxiv.org/abs/2306.08727
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts the backw
Externí odkaz:
http://arxiv.org/abs/2302.07462
Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias of neural networks. Our contributions are two-f
Externí odkaz:
http://arxiv.org/abs/2208.04924
In this paper, we revisit Korn's inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed with minimal jump terms. These minimal jump terms are identified by ch
Externí odkaz:
http://arxiv.org/abs/2207.02060
In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner for the Newton iteration of the resulting discrete system. The new appro
Externí odkaz:
http://arxiv.org/abs/2207.01425
Autor:
Williams, David M., Hong, Qingguo
The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's inequalities, as the
Externí odkaz:
http://arxiv.org/abs/2207.00695
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or empirical
Externí odkaz:
http://arxiv.org/abs/2107.04466
Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K}_1(\mathbb{D})$-norm of the solution. We show that the resulting cons
Externí odkaz:
http://arxiv.org/abs/2104.02903
Publikováno v:
In Computational Materials Science March 2024 236
Publikováno v:
MATHEMATICS OF COMPUTATION, Volume 92, Number 340, 2023, Pages 607-634
In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babuska's theory from a small inf-sup condition, similar to the famous Ladyzh
Externí odkaz:
http://arxiv.org/abs/2103.09357