Cover Image

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Zhu, Qiao, Chaikovskii, Dmitrii, Jin, Bangti, Zhang, Ye
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis 35B25, 65D17, 65N99, 68T07
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
by: Ren, Jingze, et al.
Published: (2026)

Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
by: Wang, Yifan, et al.
Published: (2023)

Neural Network Element Method for Partial Differential Equations
by: Wang, Yifan, et al.
Published: (2025)

Subspace method based on neural networks for eigenvalue problems
by: Dai, Xiaoying, et al.
Published: (2024)

Fast variable density node generation on parametric surfaces with application to mesh-free methods
by: Duh, Urban, et al.
Published: (2020)

Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis
by: Duh, Urban, et al.
Published: (2023)

Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)

Enforcing boundary conditions for physics-informed neural operators
by: Göschel, Niklas, et al.
Published: (2025)

A C^s-smooth mixed degree and regularity isogeometric spline space over planar multi-patch domains
by: Kapl, Mario, et al.
Published: (2024)

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations
by: Yuan, Long, et al.
Published: (2025)

Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
by: Franck, Emmanuel, et al.
Published: (2025)

The lowest-order Neural Approximated Virtual Element Method on polygonal elements
by: Berrone, Stefano, et al.
Published: (2024)

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
by: Codega, Gabriele, et al.
Published: (2025)

Anderson Acceleration with Truncated Gram-Schmidt
by: Tang, Ziyuan, et al.
Published: (2024)

Solving Schrödinger Equation Using Tensor Neural Network
by: Liao, Yangfei, et al.
Published: (2022)

Operator Inference for Elliptic Eigenvalue Problems
by: Li, Haoqian, et al.
Published: (2025)

ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
by: Cai, Wei, et al.
Published: (2025)

Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
by: da Veiga, Lourenço Beirão, et al.
Published: (2021)

Discontinuous hybrid neural networks for the one-dimensional partial differential equations
by: Wang, Xiaoyu, et al.
Published: (2025)

A neuron-wise subspace correction method for the finite neuron method
by: Park, Jongho, et al.
Published: (2022)

S$^2$GPT-PINNs: Sparse and Small models for PDEs
by: Ji, Yajie, et al.
Published: (2025)

All Equalities Are Equal, but Some Are More Equal Than Others: The Effect of Implementation Aliasing on the Numerical Solution to Conservation Equations
by: Trojak, Will, et al.
Published: (2019)

Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
by: Caldana, Matteo, et al.
Published: (2024)

Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs
by: Bi, Ran, et al.
Published: (2026)

Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients
by: Kröpfl, Fabian, et al.
Published: (2025)

A Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networks
by: Chen, Gaohang, et al.
Published: (2025)

An arbitrary-order fully discrete Stokes complex on general polyhedral meshes
by: Hanot, Marien-Lorenzo
Published: (2021)

Robust virtual element methods for 3D stress-assisted diffusion problems
by: Rubiano, Andres E.
Published: (2025)

Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
by: Cooley, Madison, et al.
Published: (2024)

Least Squares with Equality constraints Extreme Learning Machines for the resolution of PDEs
by: De Falco, Davide Elia, et al.
Published: (2025)

Geometric Generalization of Neural Operators from Kernel Integral Perspective
by: Han, Mingyu, et al.
Published: (2026)

A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media
by: Cui, Chen, et al.
Published: (2024)

The Neural Approximated Virtual Element Method for Elasticity Problems
by: Berrone, Stefano, et al.
Published: (2025)

A framework of discontinuous Galerkin neural networks for iteratively approximating residuals
by: Yuan, Long, et al.
Published: (2025)

Multiscale Neural Networks for Approximating Green's Functions
by: Hao, Wenrui, et al.
Published: (2024)

When can forward stable algorithms be composed stably?
by: Beltrán, Carlos, et al.
Published: (2021)

Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems
by: Guo, Shihan, et al.
Published: (2026)

An $r$-adaptive finite element method using neural networks for parametric self-adjoint elliptic problem
by: Aballay, Danilo, et al.
Published: (2025)

RONOM: Reduced-Order Neural Operator Modeling
by: Dummer, Sven, et al.
Published: (2025)

Deep Micro Solvers for Rough-Wall Stokes Flow in a Heterogeneous Multiscale Method
by: Ström, Emanuel, et al.
Published: (2025)