where 𝚵 @2,! is a vector of unique matrix elements of 𝐔 @2 defined in eq (19). Therefore, we are effectively using the feedforward neural networks of DDNN and PR-DDNN to fit the interaction DPEM 𝐔 @2 . We add the low-dimensional DPEM 𝐔 A2 at the DPEM layer, which is layer L-1.