  In this paper, we propose a novel numerical method for Path-Dependent Partial
Differential Equations (PPDEs). These equations firstly appeared in the seminal
work of Dupire [2009], 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 [2018]
to deal with these equations. 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. We then analyze several
numerical examples, many from the Financial Mathematics literature, that show
the capabilities of the method under very different situations.
