Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networks
Fuente:
arXiv
Saved in:
| Main Authors: | Tanaka, Kazuaki, Yatabe, Kohei |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Development and Analysis of Chien-Physics-Informed Neural Networks for Singular Perturbation Problems
by: Singh, Gautam, et al.
Published: (2025)
by: Singh, Gautam, et al.
Published: (2025)
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
by: Fabiani, Gianluca, et al.
Published: (2024)
by: Fabiani, Gianluca, et al.
Published: (2024)
Neural Network Element Method for Partial Differential Equations
by: Wang, Yifan, et al.
Published: (2025)
by: Wang, Yifan, et al.
Published: (2025)
Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
by: Wang, Yifan, et al.
Published: (2023)
by: Wang, Yifan, et al.
Published: (2023)
Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
by: Tahimi, Abdeladhim
Published: (2026)
by: Tahimi, Abdeladhim
Published: (2026)
A Structure-Preserving Framework for Solving Parabolic Partial Differential Equations with Neural Networks
by: Chen, Gaohang, et al.
Published: (2025)
by: Chen, Gaohang, et al.
Published: (2025)
$hp$-version $C^1$-continuous Petrov-Galerkin method for nonlinear second-order initial value problems with application to wave equations
by: Wang, Lina, et al.
Published: (2023)
by: Wang, Lina, et al.
Published: (2023)
Second-order robust parallel integrators for dynamical low-rank approximation
by: Kusch, Jonas
Published: (2024)
by: Kusch, Jonas
Published: (2024)
A robust second-order low-rank BUG integrator based on the midpoint rule
by: Ceruti, Gianluca, et al.
Published: (2024)
by: Ceruti, Gianluca, et al.
Published: (2024)
Symplectic integrators for second-order linear non-autonomous equations
by: Bader, Philipp, et al.
Published: (2017)
by: Bader, Philipp, et al.
Published: (2017)
Numerical solutions of ordinary differential equations using Spline-Integral Operator
by: Salgado, Gustavo H. O., et al.
Published: (2024)
by: Salgado, Gustavo H. O., et al.
Published: (2024)
A New Class of General Linear Method with Inherent Quadratic Stability for Solving Stiff Differential Systems
by: Gautam, Sakshi, et al.
Published: (2025)
by: Gautam, Sakshi, et al.
Published: (2025)
Splitting Schemes for ODEs with Goal-Oriented Error Estimation
by: Weyl, Erik, et al.
Published: (2026)
by: Weyl, Erik, et al.
Published: (2026)
Error analysis for learning fractional stochastic differential equations with applications in neural approximations
by: Dehshiri, Mahdi, et al.
Published: (2026)
by: Dehshiri, Mahdi, et al.
Published: (2026)
Multirate methods for ordinary differential equations
by: Günther, Michael, et al.
Published: (2025)
by: Günther, Michael, et al.
Published: (2025)
Physics-Informed Neural Networks: Bridging the Divide Between Conservative and Non-Conservative Equations
by: Neelan, Arun Govind, et al.
Published: (2025)
by: Neelan, Arun Govind, et al.
Published: (2025)
Understanding the ultraspherical spectral method
by: Cheng, Lu, et al.
Published: (2024)
by: Cheng, Lu, et al.
Published: (2024)
GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
by: Patsatzis, Dimitrios G., et al.
Published: (2024)
by: Patsatzis, Dimitrios G., et al.
Published: (2024)
Tensor Neural Network Based Machine Learning Method for Elliptic Multiscale Problems
by: Lin, Zhongshuo, et al.
Published: (2024)
by: Lin, Zhongshuo, et al.
Published: (2024)
Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
by: Bochacik, Tomasz, et al.
Published: (2024)
by: Bochacik, Tomasz, et al.
Published: (2024)
The need for accuracy and smoothness in numerical simulations
by: Mikkelsen, Carl Christian Kjelgaard, et al.
Published: (2024)
by: Mikkelsen, Carl Christian Kjelgaard, et al.
Published: (2024)
Double-activation neural network for solving parabolic equations with time delay
by: Huang, Qiumei, et al.
Published: (2024)
by: Huang, Qiumei, et al.
Published: (2024)
A Multi-Invariant Preserving Discrete Gradient Methods
by: Pu, Haodong, et al.
Published: (2026)
by: Pu, Haodong, et al.
Published: (2026)
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)
by: Aberqi, Ahmed, et al.
Published: (2026)
A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks
by: Ceruti, Gianluca, et al.
Published: (2024)
by: Ceruti, Gianluca, et al.
Published: (2024)
Multi-Order Runge-Kutta Methods or how to numerically solve initial value problems of any order
by: Petronijevic, Loris
Published: (2025)
by: Petronijevic, Loris
Published: (2025)
Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
by: Sommer, Finn, et al.
Published: (2026)
by: Sommer, Finn, et al.
Published: (2026)
RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks
by: Gattiglio, Guglielmo, et al.
Published: (2024)
by: Gattiglio, Guglielmo, et al.
Published: (2024)
Learning WENO for entropy stable schemes to solve conservation laws
by: Charles, Philip, et al.
Published: (2024)
by: Charles, Philip, et al.
Published: (2024)
Projected exponential methods for stiff dynamical low-rank approximation problems
by: Carrel, Benjamin, et al.
Published: (2023)
by: Carrel, Benjamin, et al.
Published: (2023)
Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods
by: Deeb, Ahmad, et al.
Published: (2026)
by: Deeb, Ahmad, et al.
Published: (2026)
A Biologically Motivated Finite Difference Approach for Simulating Singularly Perturbed Vertical Motion in Human Gait
by: Gupta, Shubhangini, et al.
Published: (2025)
by: Gupta, Shubhangini, et al.
Published: (2025)
Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations
by: Öffner, Philipp, et al.
Published: (2024)
by: Öffner, Philipp, et al.
Published: (2024)
Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
by: Ren, Jingze, et al.
Published: (2026)
by: Ren, Jingze, et al.
Published: (2026)
EGPT-PINN: Entropy-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conservation laws
by: Ji, Yajie, et al.
Published: (2025)
by: Ji, Yajie, et al.
Published: (2025)
Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
by: Caldana, Matteo, et al.
Published: (2024)
by: Caldana, Matteo, et al.
Published: (2024)
Parametric Numerical Integration with (Differential) Machine Learning
by: Leitao, Álvaro, et al.
Published: (2025)
by: Leitao, Álvaro, et al.
Published: (2025)
Mixed Precision Training of Neural ODEs
by: Celledoni, Elena, et al.
Published: (2025)
by: Celledoni, Elena, et al.
Published: (2025)
Polygonal Sequence-driven Triangulation Validator: An Incremental Approach to 2D Triangulation Verification
by: Sawai, Sora, et al.
Published: (2024)
by: Sawai, Sora, et al.
Published: (2024)
A Priori Adaptive Numerical Methods for Estimating Blow-up Times of Autonomous ODEs
by: Hoel, Håkon, et al.
Published: (2026)
by: Hoel, Håkon, et al.
Published: (2026)
Similar Items
-
Development and Analysis of Chien-Physics-Informed Neural Networks for Singular Perturbation Problems
by: Singh, Gautam, et al.
Published: (2025) -
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
by: Fabiani, Gianluca, et al.
Published: (2024) -
Neural Network Element Method for Partial Differential Equations
by: Wang, Yifan, et al.
Published: (2025) -
Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
by: Wang, Yifan, et al.
Published: (2023) -
Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
by: Tahimi, Abdeladhim
Published: (2026)