Cover Image

Solution of Advection Equation with Discontinuous Initial and Boundary Conditions via Physics-Informed Neural Networks

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Khosravi, Omid, Tatari, Mehdi
Format:	Preprint
Published:	2026
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Fourier-Gegenbauer Integral-Galerkin Method for Solving the Advection-Diffusion Equation With Periodic Boundary Conditions
by: Elgindy, Kareem T.
Published: (2025)

CLINN: Conservation Law Informed Neural Network for Approximating Discontinuous Solutions
by: Zeng, Weiheng, et al.
Published: (2025)

Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Discontinuity Interface
by: Cai, Zhiqiang, et al.
Published: (2023)

Observations on Recurrent Loss in the Neural Network Model of a Partial Differential Equation: the Advection-Diffusion Equation
by: Reeger, Jonah A.
Published: (2025)

Discontinuity Computing using Physics-Informed Neural Network
by: Liu, Li, et al.
Published: (2022)

Stability and Time-Step Constraints of Exponential Time Differencing Runge--Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations
by: Xu, Ziyao, et al.
Published: (2025)

Stability of Wall Boundary Condition Procedures for Discontinuous Galerkin Spectral Element Approximations of the Compressible Euler Equations
by: Hindenlang, Florian J., et al.
Published: (2019)

First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models
by: Qu, Yifan, et al.
Published: (2024)

Computing exponential of tridiagonal Toeplitz matrices with applications to numerical solution of the heat equation
by: Tatari, Mehdi, et al.
Published: (2020)

Local Randomized Neural Networks with Discontinuous Galerkin Methods for KdV-type and Burgers Equations
by: Sun, Jingbo, et al.
Published: (2024)

General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equations
by: Wang, Sen, et al.
Published: (2024)

Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks
by: Celaya, Adrian, et al.
Published: (2025)

Transformed Physics-Informed Neural Networks for The Convection-Diffusion Equation
by: Guan, Jiajing, et al.
Published: (2024)

A Unified Benchmark of Physics-Informed Neural Networks and Kolmogorov-Arnold Networks for Ordinary and Partial Differential Equations
by: Dzimah, Salvador K., et al.
Published: (2026)

PhysicsSolver: Transformer-Enhanced Physics-Informed Neural Networks for Forward and Forecasting Problems in Partial Differential Equations
by: Zhu, Zhenyi, et al.
Published: (2025)

Causal Operator Discovery in Partial Differential Equations via Counterfactual Physics-Informed Neural Networks
by: Katende, Ronald
Published: (2025)

A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs
by: Hu, Wei-Fan, et al.
Published: (2026)

Singular Layer Physics-Informed Neural Network Method for Convection-Dominated Boundary Layer Problems in Two Dimensions
by: Gie, Gung-Min, et al.
Published: (2023)

Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations
by: Andre-Sloan, Sebastien, et al.
Published: (2026)

Leveraging Lie Group Symmetries to Enhance Physics-Informed Neural Networks for the Fundamental Solution of Linear PDEs
by: Jiao, Xiaopei, et al.
Published: (2024)

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations
by: Jafarimoghaddam, Amin, et al.
Published: (2025)

Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems
by: von Danwitz, Max, et al.
Published: (2022)

A Spline-based Physics-Informed Numerical Scheme: Accurate Smooth Solutions for Differential Equations
by: Mourad, Ayman, et al.
Published: (2026)

On the Stability and Convergence of Physics Informed Neural Networks
by: Gazoulis, Dimitrios, et al.
Published: (2023)

An Efficient Solver to Helmholtz Equations by Recontruction Discontinuous Approximation
by: Zhao, Shuhai
Published: (2025)

Coupling Physics Informed Neural Networks with External Solvers
by: Halder, Rahul, et al.
Published: (2025)

Continuous Data Assimilation for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions
by: Wu, W. C., et al.
Published: (2025)

A Geometric Multigrid Preconditioner for Discontinuous Galerkin Shifted Boundary Method
by: Wichrowski, Michal
Published: (2025)

Deep Neural Network Solutions for Oscillatory Fredholm Integral Equations
by: Jiang, Jie, et al.
Published: (2024)

Projected Sobolev Natural Gradient Descent for Efficient Neural Network Solution of the Gross-Pitaevskii Equation
by: Bao, Chenglong, et al.
Published: (2025)

Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations
by: Hao, Wenrui, et al.
Published: (2024)

A Semi-Lagrangian Spherical Essentially Non-Oscillatory (SENO) Scheme for Advection Equations of S2-valued Functions
by: Leung, Shingyu
Published: (2026)

Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations
by: Zhou, Wei, et al.
Published: (2024)

H-Matrix Accelerated Direct Matrix Solver for Maxwell's Equations using the Chebyshev-based Nyström Boundary Integral Equation Method
by: Hu, Jin, et al.
Published: (2024)

Estimation of Hemodynamic Parameters via Physics Informed Neural Networks including Hematocrit Dependent Rheology
by: Sierpe, Moises, et al.
Published: (2025)

Physics Informed Neural Networks for heat conduction with phase change
by: Madir, Bahae-Eddine, et al.
Published: (2024)

Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps
by: Cai, Zhiqiang, et al.
Published: (2023)

Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions
by: Ren, Mohan, et al.
Published: (2024)

Multilevel Isogeometric Projection Stabilization via Quasi-Interpolation for Advection-Dominated Problems
by: Hasnaoui, Zakaria El, et al.
Published: (2026)

Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains
by: Sun, Yunxia, et al.
Published: (2025)