A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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A priori error bounds and optimal recovery rates are derived for a designed loss for PINNs applied to the heat equation, but the key error bound omits a needed regularity assumption and the neural network minimizer's convergence is not proven.
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Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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A priori error analysis of consistent PINNs for parabolic PDEs
A priori error bounds and optimal recovery rates are derived for a designed loss for PINNs applied to the heat equation, but the key error bound omits a needed regularity assumption and the neural network minimizer's convergence is not proven.