A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers
As nonlinearity strengthens, the accuracy advantage of discretization-based constraints becomes increasingly pronounced, with smaller optimization errors compensating for the truncation errors, and the more complex the nonlinearity and boundary conditions, the greater the advantage of GNN over MLP.
Xing Guo, Hong-Wei Tang, Ze-Wei Meng et al.
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