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.
1 a Mp V (3) avec Mj “ max xPIj |f2pxq|. En raison de la fonction r.s, řk j“1 nj « řk j“1 N ? Mj řk p“1 ? Mp “ N avec un écart au plusk, celui-ci devenant négligeable quandN
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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.