Cover Image

Numerical PDE solvers outperform neural PDE solvers

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Chatain, Patrick, Rizvi-Martel, Michael, Rabusseau, Guillaume, Oberman, Adam
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis Machine Learning 35R30 (Primary) 65M06 65M32 65C20 68T07 (Secondary)
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
by: Haugen, Emil, et al.
Published: (2025)

Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory
by: Zhang, Xifeng, et al.
Published: (2026)

A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient
by: Altybay, Arshyn
Published: (2026)

Numerical identification of the time-dependent coefficient in the heat equation with fractional Laplacian
by: Altybay, Arshyn, et al.
Published: (2025)

A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems
by: Ren, Kui, et al.
Published: (2022)

From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamics
by: Acosta-Minoli, Cesar, et al.
Published: (2026)

POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification
by: Fu, Hongfei, et al.
Published: (2016)

Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains
by: Ta, Thi Thanh Mai, et al.
Published: (2025)

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

A Convergent Numerical Algorithm for $α$-Dissipative Solutions of the Hunter-Saxton Equation
by: Christiansen, Thomas, et al.
Published: (2023)

PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problems
by: Aghaei, Alireza Afzal, et al.
Published: (2024)

Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries
by: Duprez, Michel, et al.
Published: (2025)

Reconstruction of source function in a parabolic equation using partial boundary measurements
by: Sharma, T., et al.
Published: (2025)

Numerical reconstruction of orders in coupled systems of subdiffusion equations
by: Liu, Yikan
Published: (2025)

The extended adjoint state and nonlinearity in correlation-based passive imaging
by: Nguyen, Tram Thi Ngoc
Published: (2025)

Data-Driven Discovery of Sign-Indefinite Artificial Viscosity for Linear Convection -- A Space-Time Reconvolution Perspective
by: Neelan, Arun Govind
Published: (2026)

Entropy stable conservative flux form neural networks
by: Liu, Lizuo, et al.
Published: (2024)

RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks
by: Gattiglio, Guglielmo, 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)

Reconstruction of heat relaxation index in phonon transport equation
by: Chen, Peiyi, et al.
Published: (2025)

Reconstructing the thermal phonon transmission coefficient at solid interfaces in the phonon transport equation
by: Gamba, Irene M, et al.
Published: (2020)

A non-iterative domain decomposition time integrator combined with discontinuous Galerkin space discretizations for acoustic wave equations
by: Buchholz, Tim, et al.
Published: (2025)

A Carleman Semi-Discrete Convexification Method Combined With Deep Learning for Electrical Impedance Tomography
by: Klibanov, Michael V., et al.
Published: (2026)

GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
by: Patsatzis, Dimitrios G., et al.
Published: (2024)

Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
by: Cao, Shuhao, et al.
Published: (2024)

A numerical view on α-dissipative solutions of the Hunter-Saxton equation
by: Christiansen, Thomas, et al.
Published: (2024)

Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
by: Guth, Philipp A., et al.
Published: (2022)

An Efficient Numerical Scheme for a Time-Fractional Burgers Equation with Caputo-Prabhakar Derivative
by: Singh, Deeksha, et al.
Published: (2024)

Numerical reconstructions of a source term in a mobile-immobile diffusion model from the partial interior observation
by: Yang, Zhiwei, et al.
Published: (2025)

Efficient Numerical Reconstruction of Wave Equation Sources via Droplet-Induced Asymptotics
by: Hou, Shutong, et al.
Published: (2026)

Error estimates of fully semi-Lagrangian schemes for diffusive conservation laws
by: Takemura, Haruki
Published: (2025)

Error estimates for semi-Lagrangian schemes with higher-order interpolation for conservation laws with dispersive terms
by: Takemura, Haruki
Published: (2025)

Mathematical analysis and symmetric fractional-order reduction method for diffusion-wave equations
by: Cen, Dakang, et al.
Published: (2026)

Numerical study on a multi-dimensional pressureless Euler-type model with non-local interactions and chemotaxis for collective cell migration
by: Menci, Marta, et al.
Published: (2025)

Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations
by: Bir, Bikram, et al.
Published: (2026)

Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time
by: Zhou, Han, et al.
Published: (2023)

Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws
by: Liu, Lizuo, et al.
Published: (2025)

Backward problem for a degenerate viscous Hamilton-Jacobi equation: stability and numerical identification
by: Chorfi, S. E., et al.
Published: (2026)

Unique continuation for the wave equation based on a discontinuous Galerkin time discretization
by: Burman, Erik, et al.
Published: (2024)

Stable Volume Dissipation for High-Order Finite-Difference and Spectral-Element Methods with the Summation-by-Parts Property
by: Bercik, Alex, et al.
Published: (2025)