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.
Structure preserving pinn for solving time dependent pdes with periodic boundary.arXiv preprint arXiv:2404.16189, 2024
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HSPINN enforces Dirichlet and periodic BCs exactly via analytical lifting and masking, applies adaptive softmax weighting to soft loss terms for PDE residuals, and reports faster convergence and higher accuracy than standard PINNs on Poisson, Burgers, and convection problems.
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Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds
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.
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Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving
HSPINN enforces Dirichlet and periodic BCs exactly via analytical lifting and masking, applies adaptive softmax weighting to soft loss terms for PDE residuals, and reports faster convergence and higher accuracy than standard PINNs on Poisson, Burgers, and convection problems.