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.
Generic bounds on the approximation error for physics-informed (and) operator learning.arXiv preprint arXiv:2205.11393, 2022
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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.