The terminology/notation in the first paragrph of the Formulation section seems very confusing, and does not seem to align up with how things are defined in Models and equations section (or in the Notations section).
E.g. x is defined as neural network input or spatial location in Notation, but here it seems to be a solution to u. Should x actually be f(x;$\theta$) or u(x; $\theta$)?
The terminology/notation in the first paragrph of the Formulation section seems very confusing, and does not seem to align up with how things are defined in Models and equations section (or in the Notations section).
E.g. x is defined as neural network input or spatial location in Notation, but here it seems to be a solution to u. Should x actually be f(x;$\theta$) or u(x; $\theta$)?