(because machine learning is much better for interpolation than for extrapolation). A problem with normal machine-learned PESs arises in asymptotic regions because such regions are infinite and therefore are not necessarily improved by adding an additional (necessarily finite) amount of additional data. In PM-DDNN, we circumvent this difficulty by introducing the parametrically managed activation function, and therefore in asymptotic regions, the, and the DPEM reduces to the lower-dimensional DPEM, which is 𝚵 % . In that way, as long as we have a physical a lowerdimensional DPEM, the PM-DDNN results will be physical even in asymptotic regions.