Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
Fuente:
arXiv
Saved in:
| Main Authors: | Hillebrecht, Birgit, Unger, Benjamin |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Overlap Splines and Meshless Finite Difference Methods
by: Davydov, Oleg
Published: (2023)
by: Davydov, Oleg
Published: (2023)
A Minimal Perturbation Approach For The Rectangular Multiparameter Eigenvalue Problem
by: Han, Shanheng, et al.
Published: (2025)
by: Han, Shanheng, et al.
Published: (2025)
Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs
by: Dũng, Dinh
Published: (2025)
by: Dũng, Dinh
Published: (2025)
Sampling recovery in Bochner spaces and applications to parametric PDEs
by: Bartel, Felix, et al.
Published: (2024)
by: Bartel, Felix, et al.
Published: (2024)
Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with Caputo fractional Laplacian and variable coefficient wave number $μ$
by: Adriani, Andrea, et al.
Published: (2024)
by: Adriani, Andrea, et al.
Published: (2024)
Near-best univariate spline discrete quasi-interpolants on non-uniform partitions
by: Barrera, D., et al.
Published: (2004)
by: Barrera, D., et al.
Published: (2004)
Sparsity for parametric PDEs with log-gamma random inputs and applications
by: Dũng, Dinh, et al.
Published: (2026)
by: Dũng, Dinh, et al.
Published: (2026)
Modal-Rectification-Based Directional Edge Diffusion for Cartesian Convection--Diffusion Problems
by: Bomisso, Gossrin Jean-Marc, et al.
Published: (2026)
by: Bomisso, Gossrin Jean-Marc, et al.
Published: (2026)
A Trefftz Continuous Galerkin method for Helmholtz problems
by: Galante, Nicola, et al.
Published: (2025)
by: Galante, Nicola, et al.
Published: (2025)
Stability of the Stokes projection on weighted spaces and applications
by: Duran, Ricardo G., et al.
Published: (2019)
by: Duran, Ricardo G., et al.
Published: (2019)
Reliable eigenspace error estimation using source error estimators
by: Gopalakrishnan, Jay, et al.
Published: (2026)
by: Gopalakrishnan, Jay, et al.
Published: (2026)
Superconvergence points of Hermite spectral interpolation
by: Wang, Haiyong, et al.
Published: (2025)
by: Wang, Haiyong, et al.
Published: (2025)
Optimal Compactly Supported Functions in Sobolev Spaces
by: Schaback, Robert
Published: (2024)
by: Schaback, Robert
Published: (2024)
The numerical linear algebra of weights: from the spectral analysis to conditioning and preconditioning in the Laplacian case
by: Bruno, Ludovico Bruni, et al.
Published: (2023)
by: Bruno, Ludovico Bruni, et al.
Published: (2023)
A new flow dynamic approach for Wasserstein gradient flows
by: Cheng, Qing, et al.
Published: (2024)
by: Cheng, Qing, et al.
Published: (2024)
A priori error analysis of consistent PINNs for parabolic PDEs
by: Mishra, Shiv, et al.
Published: (2025)
by: Mishra, Shiv, et al.
Published: (2025)
Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs
by: Dũng, Dinh
Published: (2026)
by: Dũng, Dinh
Published: (2026)
A new interpolated pseudodifferential preconditioner for the Helmholtz equation in heterogeneous media
by: Acosta, Sebastian, et al.
Published: (2024)
by: Acosta, Sebastian, et al.
Published: (2024)
Error Estimates for Discontinuous Galerkin Approximations to the Vlasov-Unsteady Stokes System
by: Hutridurga, Harsha, et al.
Published: (2024)
by: Hutridurga, Harsha, et al.
Published: (2024)
Partial Differential Equations on Low-Dimensional Structures
by: Chomienia, Łukasz
Published: (2024)
by: Chomienia, Łukasz
Published: (2024)
A discontinuous Galerkin method for elliptic-hyperbolic equations
by: Perinati, Chiara, et al.
Published: (2026)
by: Perinati, Chiara, et al.
Published: (2026)
Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
by: Imbert-Gérard, Lise-Marie, et al.
Published: (2024)
by: Imbert-Gérard, Lise-Marie, et al.
Published: (2024)
The Biharmonic Heat Equation with General Dynamic Boundary Conditions
by: Chorfi, S. E., et al.
Published: (2026)
by: Chorfi, S. E., et al.
Published: (2026)
Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
by: Kaltenbach, Alex, et al.
Published: (2024)
by: Kaltenbach, Alex, et al.
Published: (2024)
Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications
by: Sablonniere, Paul
Published: (2004)
by: Sablonniere, Paul
Published: (2004)
Computing Stokes flows in periodic channels via rational approximation
by: Xue, Yidan
Published: (2024)
by: Xue, Yidan
Published: (2024)
Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations
by: Berselli, Luigi C., et al.
Published: (2023)
by: Berselli, Luigi C., et al.
Published: (2023)
Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
by: Gimperlein, Heiko, et al.
Published: (2025)
by: Gimperlein, Heiko, et al.
Published: (2025)
Error analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations
by: Berselli, Luigi C., et al.
Published: (2025)
by: Berselli, Luigi C., et al.
Published: (2025)
Computation of 2D Stokes flows via lightning and AAA rational approximation
by: Xue, Yidan, et al.
Published: (2023)
by: Xue, Yidan, et al.
Published: (2023)
A convergent interacting particle method for computing KPP front speeds in random flows
by: Zhang, Tan, et al.
Published: (2023)
by: Zhang, Tan, et al.
Published: (2023)
Block Jacobi/Gauss-Seidel preconditioning for GLT sequences, and GLH sequences
by: Garoni, Carlo, et al.
Published: (2026)
by: Garoni, Carlo, et al.
Published: (2026)
Finite element and box-method discretizations for fractional elliptic problems with quadrature and mass lumping
by: Almeida-Sousa, Kelvin J. R., et al.
Published: (2026)
by: Almeida-Sousa, Kelvin J. R., et al.
Published: (2026)
Finite element approximation to linear, second order, parabolic problems with $L^1$ data
by: Barrenechea, Gabriel, et al.
Published: (2025)
by: Barrenechea, Gabriel, 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)
by: Constantin, Loïc, et al.
Published: (2026)
Structure-preserving scheme for 1D KWC system
by: Okumura, Makoto, et al.
Published: (2025)
by: Okumura, Makoto, et al.
Published: (2025)
Stabilized velocity post-processings for Darcy flow in heterogeneous porous media
by: Correa, Maicon R., et al.
Published: (2025)
by: Correa, Maicon R., et al.
Published: (2025)
Optimal properties of tensor product of B-bases
by: Delgado, Jorge, et al.
Published: (2025)
by: Delgado, Jorge, et al.
Published: (2025)
An Optimal Weighted Least-Squares Method for Operator Learning
by: Turnage, John, et al.
Published: (2025)
by: Turnage, John, et al.
Published: (2025)
A time dependent fractional order diffusion equation with constant diffusivity matrix
by: Catoe, T., et al.
Published: (2026)
by: Catoe, T., et al.
Published: (2026)
Similar Items
-
Overlap Splines and Meshless Finite Difference Methods
by: Davydov, Oleg
Published: (2023) -
A Minimal Perturbation Approach For The Rectangular Multiparameter Eigenvalue Problem
by: Han, Shanheng, et al.
Published: (2025) -
Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs
by: Dũng, Dinh
Published: (2025) -
Sampling recovery in Bochner spaces and applications to parametric PDEs
by: Bartel, Felix, et al.
Published: (2024) -
Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with Caputo fractional Laplacian and variable coefficient wave number $μ$
by: Adriani, Andrea, et al.
Published: (2024)