Collocation approximation by deep neural ReLU networks for parametric
elliptic PDEs with lognormal inputs
Collocation approximation by deep neural ReLU networks for parametric
elliptic PDEs with lognormal inputs
We obtained convergence rates of the collocation approximation by deep ReLU neural networks of the solution $u$ to elliptic PDEs with lognormal inputs, parametrized by $\boldsymbol{y}$ from the non-compact set $\mathbb{R}^\infty$. The approximation error is measured in the norm of the Bochner space $L_2(\mathbb{R}^\infty, V, \gamma)$, where $\gamma$ is the …