Review for NeurIPS paper: Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning

Weaknesses: The authors restrict to affine-linear parameters, but this restriction is not a requirement of the methodology and it is unclear from the text why the restriction was put in place. Is the purpose solely to narrow the scope of the analysis, or is there some performance loss for more general coefficients? It would be useful for the authors to comment in the paper on why this restriction is imposed. Similarly the theoretical results proven apply only to the example from Section 3.3 with a specific initial condition. A more general result would be preferable, particularly since the highest dimension application the authors have provided is actually for a different initial condition (though, of course, the input dimension for the parabaloid initial condition is still rather high). However a more general result may not be straightforward to derive.