Results 171 to 180 of about 543 (203)

SAOT: An Enhanced Locality-Aware Spectral Transformer for Solving PDEs

AAAI Conference on Artificial Intelligence
Neural operators have shown great potential in solving a family of Partial Differential Equations (PDEs) by modeling the mappings between input and output functions.
Chenhong Zhou, Jie Chen, Zaifeng Yang
semanticscholar   +1 more source

Adaptive Mamba Neural Operators

arXiv.org
Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications.
Ze-Yuan Song, Zhe-Yu Jiang
semanticscholar   +1 more source

Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks

arXiv.org
Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the neural network ...
F. Mostajeran, S. Faroughi
semanticscholar   +1 more source

Monte Carlo-Type Neural Operator for One-Dimensional Differential Equations

International Conference on Machine Learning and Applications
The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral operator using ...
S. E. Choutri, Prajwal Chauhan, Othmane Mazhar, S. Jabari   +3 more
semanticscholar   +1 more source

Monte Carlo-Type Neural Operator for Differential Equations

arXiv.org
The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral operator using ...
S. E. Choutri, Prajwal Chauhan, Othmane Mazhar, S. Jabari   +3 more
semanticscholar   +1 more source

Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data

arXiv.org
Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and limited by sparse
Xingyu Chen, Junxiu An, Junjian Guo, Yu-Qian Zhou   +3 more
semanticscholar   +1 more source

M2M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations need

arXiv.org
Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the solution, where
Aoming Liang, Zhaoyang Mu, Peng-Xiao Lin, Cong Wang, Mingming Ge, Ling Shao, Dixia Fan, Hao Tang   +7 more
semanticscholar   +1 more source

MINPO: Memory-Informed Neural Pseudo-Operator to Resolve Nonlocal Spatiotemporal Dynamics

arXiv.org
Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating convolution integrals, whose cost increases quickly with kernel ...
F. Mostajeran, Aruzhan Tleubek, S. Faroughi   +2 more
semanticscholar   +1 more source

Methods for Solving Elliptic PDEs in Spherical Coordinates

SIAM Journal on Applied Mathematics, 2008
G. Dassios, A. Fokas
semanticscholar   +1 more source

A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon

, 2010
S. Smitheman, E. Spence, A. Fokas
semanticscholar   +1 more source