Before revision:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
After revision:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization used for the FBSDEs. As a result, a Richardson extrapolation technique over time discretizations can be used to enhance the accuracy of the DNN solutions. For time oscillatory solutions, a multiscale DNN is shown to improve the performance of the FBSDE DNN for high frequencies .