Hessian-guided adaptive collocation sampling for PINNs, backed by a 1D quadrature error bound, achieves lower L2 errors than uniform, residual-based, and gradient-based sampling on two test PDEs.
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M\'ethode de quadrature pour les PINNs fond\'ee th\'eoriquement sur la hessienne des r\'esiduels
Hessian-guided adaptive collocation sampling for PINNs, backed by a 1D quadrature error bound, achieves lower L2 errors than uniform, residual-based, and gradient-based sampling on two test PDEs.