4 problems

The examples concern neural-network approximation of solution operators for parametric partial differential equations, including the parametric stationary Boussinesq equations, wit…

Let $\cU$ be the parameter domain, let $\cV$ be the target space, and let $L^{\infty}(\cU;\cV)$ denote the space of essentially bounded $\cV$-valued functions on $\cU$. Suppose the…

Let the LRV strategy denote the algorithm discussed in the paper for approximating solutions of parametric PDE problems, and let $L^\infty$-norm error measure the uniform approxima…

Let $D\subset\mathbb{R}^2$ be a bounded polygon with vertices ${\bf c}_j$, and let $K^k_{\theta+1}(D)$ denote the Kondrat'ev space defined by … where…