Cover Image

Robust error estimates of PINN in one-dimensional boundary value problems for linear elliptic equations

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Yoo, Jihahm, Lee, Haesung
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis Analysis of PDEs Primary: 34B05, 35A15, Secondary: 68T07, 65L10
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Quantitative analysis for $L^2$-estimates in linear elliptic equations via divergence-free transformation
by: Lee, Haesung
Published: (2025)

A priori error estimates for the $θ$-method for the flow of nonsmooth velocity fields
by: Ciampa, Gennaro, et al.
Published: (2025)

Resolvent approaches to elliptic regularity in stationary Fokker-Planck equations
by: Lee, Haesung
Published: (2026)

A PINNs approach for the computation of eigenvalues in elliptic problems
by: Bonder, Julian Fernandez, et al.
Published: (2025)

An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non cartesian grids
by: Cortopassi, Tommaso
Published: (2024)

Hypernetwork-Conditioned WENO5 Conservative-Form CNNs for One-Dimensional Conservation Laws
by: Chen, Yongsheng, et al.
Published: (2026)

Theory of shifts, shocks, and the intimate connections to $L^2$-type a posteriori error analysis of numerical schemes for hyperbolic problems
by: Giesselmann, Jan, et al.
Published: (2023)

Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
by: Alejo, Miguel Á., et al.
Published: (2024)

Solving the Fisher nonlinear differential equations via Physics-Informed Neural Networks: A Comprehensive Retraining Study and Comparative Analysis with the Finite Difference Method
by: Aberqi, Ahmed, et al.
Published: (2026)

Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
by: Sommer, Finn, et al.
Published: (2026)

Extension and neural operator approximation of the electrical impedance tomography inverse map
by: de Hoop, Maarten V., et al.
Published: (2025)

Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
by: Yang, Hee Jun, et al.
Published: (2025)

Improved error estimates for low-regularity integrators using space-time bounds
by: Ruff, Maximilian
Published: (2025)

Analysis of linear elliptic equations with general drifts and $L^1$-zero-order terms
by: Lee, Haesung
Published: (2024)

Nonlinear fractional-periodic boundary value problems with Hilfer fractional derivative: existence and numerical approximations of solutions
by: Goedegebure, Niels, et al.
Published: (2026)

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

Structure-preserving LDG methods for linear and nonlinear transport equations with gradient noise
by: Christiansen, Thomas, et al.
Published: (2026)

Mathematical models for nonlinear ultrasound contrast imaging with microbubbles
by: Nikolić, Vanja, et al.
Published: (2024)

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

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

Asymptotically compatible entropy-consistent discretization for a class of nonlocal conservation laws
by: De Nitti, Nicola, et al.
Published: (2025)

Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networks
by: Esteve-Yagüe, Carlos, et al.
Published: (2024)

Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems
by: Lin, Zhongshuo, et al.
Published: (2024)

Deterministic particle method for nonlinear nonlocal scalar balance equations
by: Radici, Emanuela, et al.
Published: (2024)

Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks
by: Adcock, Ben, et al.
Published: (2022)

Neural Preconditioned Born Series: A Metric-Matched Framework for Learning-based Preconditioners
by: Wang, Juntao, et al.
Published: (2026)

A numerical Bernstein splines approach for nonlinear initial value problems with Hilfer fractional derivative
by: Goedegebure, Niels, et al.
Published: (2025)

Well-posedness of a Variable-Exponent Telegraph Equation Applied to Image Despeckling
by: Majee, Sudeb, et al.
Published: (2024)

Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions
by: Ruff, Maximilian, et al.
Published: (2023)

Maximal regularity for generalized boundary conditions in time
by: Arendt, Wolfgang, et al.
Published: (2025)

Learning WENO for entropy stable schemes to solve conservation laws
by: Charles, Philip, et al.
Published: (2024)

Multiharmonic algorithms for contrast-enhanced ultrasound
by: Nikolić, Vanja, et al.
Published: (2025)

Weak Adversarial Neural Pushforward Method for Fractional Fokker-Planck Equations
by: He, Andrew Qing, et al.
Published: (2026)

Neural Shape Operator Surrogates -- Expression Rate Bounds
by: Harbrecht, Helmut, et al.
Published: (2026)

Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
by: Li, Ziqian, et al.
Published: (2024)

A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
by: Cao, Jiachuan, et al.
Published: (2026)

Transport based particle methods for the Fokker-Planck-Landau equation
by: Ilin, Vasily, et al.
Published: (2024)

Linear stability of discrete shock profiles for systems of conservation laws
by: Coeuret, Lucas
Published: (2023)

Nonlinear orbital stability of stationary discrete shock profiles for scalar conservation laws
by: Coeuret, Lucas
Published: (2024)

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