Resumo: In this talk, we will present several extensions of the Deep Galerkin Method (DGM), originally introduced in Sirignano and Spiliopoulos (2018), where they propose a deep learning algorithm to solve Partial Differential Equations. In the Fokker-Planck setting, our approach involves reparameterizing the solution as the exponential of a neural network appropriately normalized to ensure that it is both positive and integrates one. We also extend the DGM algorithm to solve for the value function and the optimal control simultaneously in the Hamilton-Jacobi-Bellman PDEs by characterizing both as deep neural networks. Training the networks is performed by taking alternating stochastic gradient descent steps for the two functions, a technique similar in spirit to policy improvement algorithms. Finally, we present 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 Itô calculus was developed to deal with path-dependence in Mathematical Finance. More specifically, we generalize the DGM 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 that show the capabilities of the method under very different situations.