Derives computable two-sided a posteriori error bounds for PINN approximations of ODEs using localized strong monotonicity for lower bounds and one-sided Lipschitz for upper bounds.
Generic bounds on the approximation error for physics-informed (and) operator learning.arXiv preprint arXiv:2205.11393, 2022
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
years
2026 2verdicts
UNVERDICTED 2representative citing papers
PINN residuals serve as an off-grid probe to adaptively refine meshes before a finite-difference solve, yielding lower error with fewer degrees of freedom than uniform refinement on the 1D Burgers equation.
citing papers explorer
-
Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers
PINN residuals serve as an off-grid probe to adaptively refine meshes before a finite-difference solve, yielding lower error with fewer degrees of freedom than uniform refinement on the 1D Burgers equation.