Learn English – Is ‘there is’ grammatically correct in this sentence

"There is" is perfectly valid in that sentence.

The primary grammatical problem with that sentence is the extra "on":

There is currently no available on large-scale solution that ...

Large-scale is a modifier to solution, and does not need a preposition to introduce it.

As pointed out elsewhere, you may also wish to simplify the sentence depending on what you want to emphasize. As written, the words currently and available serve to give the impression that at some not-too-distant time, a suitable solution may become available. If you remove those words, you remove that impression as well:

There is no large-scale solution that ...

This reads as a blanket statement, implying that such a solution may in fact be impossible.

If large scale is intended to refer to how available the solution is, rather than to the capability of the solution itself, then the sentence needs to be reworded to clearly apply the modifier to the correct element:

There is currently no solution available on a large scale that ...