Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Cao, Shuhao"'
In this work, we propose an Operator Learning (OpL) method for solving boundary value inverse problems in partial differential equations (PDEs), focusing on recovering diffusion coefficients from boundary data. Inspired by the classical Direct Sampli
Externí odkaz:
http://arxiv.org/abs/2411.05341
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training expenses, and
Externí odkaz:
http://arxiv.org/abs/2405.17211
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an $M$-matrix) o
Externí odkaz:
http://arxiv.org/abs/2402.13347
Autor:
Cao, Shuhao, Qin, Lizhen
Publikováno v:
SIAM J. Sci. Comput. 46 (2024), no.1, A376-A398
A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested on some $4$
Externí odkaz:
http://arxiv.org/abs/2212.04079
Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications
Externí odkaz:
http://arxiv.org/abs/2210.10890
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operat
Externí odkaz:
http://arxiv.org/abs/2209.14977
We introduce a nonconforming hybrid finite element method for the two-dimensional vector Laplacian, based on a primal variational principle for which conforming methods are known to be inconsistent. Consistency is ensured using penalty terms similar
Externí odkaz:
http://arxiv.org/abs/2206.10567
Publikováno v:
Mathematical Models and Methods in Applied Sciences 33, no. 03 (2023): 455-503
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential obstacle f
Externí odkaz:
http://arxiv.org/abs/2202.09987
"Masked Autoencoders (MAE) Are Scalable Vision Learners" revolutionizes the self-supervised learning method in that it not only achieves the state-of-the-art for image pre-training, but is also a milestone that bridges the gap between visual and ling
Externí odkaz:
http://arxiv.org/abs/2202.03670
The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix-valued a
Externí odkaz:
http://arxiv.org/abs/2109.09948