Before revision:  These equations firstly appeared in the seminal work of \mbox{%DIFAUXCMD fito_dupire  , where the functional It\^o calculus was developed to deal with path-dependent financial derivatives contracts  ]  . The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE.
After revision:  These equations firstly appeared in the seminal work of \mbox{%DIFAUXCMD fito_dupire , where the functional It\^o calculus was developed to deal with path-dependent financial derivatives contracts . More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos ] . The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE.