I have read through the draft manuscript. Overall I thought it was well written and fits the style of a JOSS paper. In addition to a few minor things included in this pr https://github.com/SGpp/DisCoTec/pull/136, I have a few suggestions listed below
A reference or two for the 'sparse grid combination technique' would be useful early on.
In the summary you say 'DisCoTec demonstrates its superiority' without making it clear what you are comparing it with. Moreover, does 'superiority' refer to accuracy, resource use, efficiency, etc?
Acronyms (such as HPC, UQ etc) should be defined before use.
The 'Statement of need' would benefit from references that cover the curse of dimensionality and the approaches that attempt to deal with it.
When you say 'multi-scale methods ... provide an alternative approach to address the curse of dimensionality' - if you can do so compactly, it would be good to explain how they achieve this.
When you say 'some other implementations of the sparse grid combination technique are available' - references should be provided if possible.
The second paragraph of the 'Statement of need' largely repeats material from the 'Summary' and could (in my opinion) be deleted.
I mentioned this already in https://github.com/SGpp/DisCoTec/issues/134, but care needs to be taken to define all mathematical notation. For example, in the combination formula, $f^{(s)}$, $f{\vec{\ell}}$ and $c{\vec{\ell}}$ are defined, but not $\vec{\ell}$ or $\mathcal{I}$.
This doesn't necessarily need to go in the paper, but could you explain how using OpenMP decreases the memory footprint?
In a couple of places, you provide links to github repositories that could (and perhaps should) be made into full references in the bibliography.
When mentioning spack - you could indicate that the purpose of this is to simplify installation on HPC systems.
On line 82: 'The C++ code SG++ allows to...' - allows what/who to?
This issue relates to ongoing reviews at https://github.com/openjournals/joss-reviews/issues/7018.
I have read through the draft manuscript. Overall I thought it was well written and fits the style of a JOSS paper. In addition to a few minor things included in this pr https://github.com/SGpp/DisCoTec/pull/136, I have a few suggestions listed below