A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional
  Nonlinear Parabolic Partial Differential Equations
Endah Rokhmati Merdika Putri Muhammad Luthfi Shahab Mohammad Iqbal Imam Mukhlash Amirul Hakam Lutfi Mardianto Hadi Susanto
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.