Correction to: Humanities and Social Sciences Communications https://doi.org/10.1057/s41599-022-01048-0, published online 26 January 2022.

The article’s title has been corrected in the PDF and online versions to remove ambiguity.

The original read: Whether growth of military hard power back up growth of monetary soft power via data-driven probabilistic optimal relations?

The revised title reads: Does the growth of military hard power back up the growth of monetary soft power via data-driven probabilistic optimal relations?