Cover Image

Two-scale Neural Networks for Partial Differential Equations with Small Parameters

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Zhuang, Qiao, Yao, Chris Ziyi, Zhang, Zhongqiang, Karniadakis, George Em
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis Machine Learning Computational Physics 65N35, 35B25 I.2.6
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters
by: Zhuang, Qiao, et al.
Published: (2026)

Active Learning Based Sampling for High-Dimensional Nonlinear Partial Differential Equations
by: Gao, Wenhan, et al.
Published: (2021)

A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term
by: Shiromani, Ram, et al.
Published: (2024)

A simple and fast finite difference method for the integral fractional Laplacian of variable order
by: Hao, Zhaopeng, et al.
Published: (2024)

Discontinuous Galerkin approximation for a Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
by: Lepe, Felipe, et al.
Published: (2025)

A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
by: Lepe, Felipe, et al.
Published: (2025)

Mesh-free numerical method for Dirichlet eigenpairs of the Laplacian with potential
by: Manea, Dragoş
Published: (2026)

Modal-Rectification-Based Directional Edge Diffusion for Cartesian Convection--Diffusion Problems
by: Bomisso, Gossrin Jean-Marc, et al.
Published: (2026)

Linearization-based direct reconstruction for EIT using triangular Zernike decompositions
by: Autio, Antti, et al.
Published: (2024)

FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation
by: Hernández-Santamaría, Víctor, et al.
Published: (2023)

Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
by: Khan, Arbaz, et al.
Published: (2024)

Legendre Expansions of Products of Functions with Applications to Nonlinear Partial Differential Equations
by: Djellouli, Rabia, et al.
Published: (2021)

On the relation between Galerkin approximations and canonical best-approximations of solutions to some non-linear Schrödinger equations
by: Hassan, Muhammad, et al.
Published: (2025)

Higher-Order Generalized Finite Differences for Variable Coefficient Diffusion Operators
by: Kraus, Heinrich, et al.
Published: (2023)

Ultra-weak least squares discretizations for unique continuation and Cauchy problems
by: Monsuur, Harald, et al.
Published: (2024)

Explicit Two-Sided Eigenvalue Bounds for Schrödinger Operators with Singular Potentials via Finite Element Method
by: Liu, Xuefeng
Published: (2026)

Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and minimal regularity
by: Ern, Alexandre, et al.
Published: (2019)

Convergent Sixth-order Compact Finite Difference Method for Variable-Coefficient Elliptic PDEs in Curved Domains
by: Han, Bin, et al.
Published: (2025)

Local electrical impedance tomography via projections
by: Jääskeläinen, A., et al.
Published: (2026)

Projection-based preprocessing for electrical impedance tomography to reduce the effect of electrode contacts
by: Jääskeläinen, Altti, et al.
Published: (2024)

Solving elliptic PDEs in unbounded domains
by: Arjmand, Doghonay, et al.
Published: (2024)

A kernel-free boundary integral method for elliptic interface problems on surfaces
by: Yin, Pengsong, et al.
Published: (2025)

Generative Reduced Basis Method
by: Nguyen, Ngoc Cuong
Published: (2024)

Convergence of Finite Difference Methods for Poisson's Equation with Interfaces
by: Liu, Xu-Dong, et al.
Published: (2001)

High-order, Compact, and Symmetric Finite Difference Methods for a $d$-Dimensional Hypercube
by: Feng, Qiwei, et al.
Published: (2025)

Underdetermined Fourier Extensions for Surface Partial Differential Equations
by: Venn, Daniel R., et al.
Published: (2024)

Mesh-Intrinsic GFEM: High-Order Smoothness on $C^0$ Unstructured Meshes
by: Tian, Rong
Published: (2026)

$d$-dimensional extension of a penalization method for Neumann or Robin boundary conditions: a boundary layer approach and numerical experiments
by: Bensiali, Bouchra, et al.
Published: (2024)

At the intersection of Numerical Analysis and Spectral Geometry
by: Nigam, Nilima
Published: (2025)

Physics-Informed Learning of Microvascular Flow Models using Graph Neural Networks
by: Botta, Paolo, et al.
Published: (2025)

The numerical solution of the Dirichlet generalized and classical harmonic problems for irregular n-sided pyramidal domains by the method of probabilistic solutions
by: Zakradze, M., et al.
Published: (2025)

The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution
by: Zakradze, Mamuli, et al.
Published: (2024)

Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
by: Glaubitz, Jan, et al.
Published: (2025)

A time dependent fractional order diffusion equation with constant diffusivity matrix
by: Catoe, T., et al.
Published: (2026)

Two Dimensional Fourier Continuation for Domains with Corners
by: Bruno, Oscar P., et al.
Published: (2026)

A data-driven method for parametric PDE Eigenvalue Problems using Gaussian Process with different covariance functions
by: Alghamdi, Moataz, et al.
Published: (2023)

Solving the fully nonlinear Monge-Ampère equation using the Legendre-Kolmogorov-Arnold Network method
by: Hu, Bingcheng, et al.
Published: (2025)

A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional $p$-Laplacian of functions defined on $\mathbb R^n$
by: Constantin, Loïc, et al.
Published: (2026)

Numerical solution of 2D boundary value problems on merged Voronoi-Delaunay meshes
by: Chernyshov, M. M., et al.
Published: (2025)

Sampling recovery in Bochner spaces and applications to parametric PDEs
by: Bartel, Felix, et al.
Published: (2024)