H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
Complexity dependent error rates for physics-informed statistical learning via the small-ball method
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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.