We propose a new method, called a deep-genetic algorithm (deep-GA), to accelerate the performance of the so-called deep-BSDE method, which is a deep learning algorithm to solve high dimensional partial differential equations through their corresponding backward stochastic differential equations (BSDEs). Recognizing the sensitivity of the solver to the initial guess selection, we embed a genetic algorithm (GA) into the solver to optimize the selection. We aim to achieve faster convergence for the nonlinear PDEs on a broader interval than deep-BSDE. Our proposed method is applied to two nonlinear parabolic PDEs, i.e., the Black-Scholes (BS) equation with default risk and the Hamilton-Jacobi-Bellman (HJB) equation. We compare the results of our method with those of the deep-BSDE and show that our method provides comparable accuracy with significantly improved computational efficiency.

翻译：我们提出了一种称为深度遗传算法（Deep-GA）的新方法，用于加速所谓深度BSDE方法的性能。深度BSDE方法是一种通过相应倒向随机微分方程（BSDE）求解高维偏微分方程的深度学习算法。认识到求解器对初始猜测选择的敏感性，我们将遗传算法（GA）嵌入求解器中以优化该选择。我们的目标是在比深度BSDE更广泛的区间上实现非线性偏微分方程的更快收敛。所提出的方法应用于两个非线性抛物型偏微分方程，即包含违约风险的Black-Scholes（BS）方程和Hamilton-Jacobi-Bellman（HJB）方程。我们将该方法的结果与深度BSDE的结果进行比较，并表明我们的方法在保持相当精度的同时，显著提高了计算效率。