Zobrazeno 1 - 10
of 292
pro vyhledávání: '"65L15"'
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace. Then the dis
Externí odkaz:
http://arxiv.org/abs/2412.02586
With the rapid development of machine learning, numerical discretization methods based on deep neural networks have been widely used in many fields, especially in solving high-dimensional problems where traditional methods face bottlenecks. However,
Externí odkaz:
http://arxiv.org/abs/2410.13358
Autor:
Okitsu, Kouhei
Behavior of X-rays diffracted in a perfect or quasi-perfect crystal can be described by the dynamical theory of X-ray diffraction. Study on the two-beam cases in which only transmitted and one reflected X-ray beams are strong has a history of one hun
Externí odkaz:
http://arxiv.org/abs/2409.17211
We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in reformula
Externí odkaz:
http://arxiv.org/abs/2409.01520
In this paper, we present some enhanced error estimates for augmented subspace methods with the nonconforming Crouzeix-Raviart (CR) element. Before the novel estimates, we derive the explicit error estimates for the case of single eigenpair and multi
Externí odkaz:
http://arxiv.org/abs/2405.00399
In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent field itera
Externí odkaz:
http://arxiv.org/abs/2404.19249
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means that we use
Externí odkaz:
http://arxiv.org/abs/2404.07805
In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the tensor neu
Externí odkaz:
http://arxiv.org/abs/2403.16380
This study proposes a class of augmented subspace schemes for the weak Galerkin (WG) finite element method used to solve eigenvalue problems. The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh a
Externí odkaz:
http://arxiv.org/abs/2401.04063
Publikováno v:
Mathematical Biosciences and Engineering 2024, Volume 21, Issue 4: 5360-5393
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth a
Externí odkaz:
http://arxiv.org/abs/2312.13477