Endah R.M. Putri, Muhammad L. 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. © 2023 Elsevier Ltd
Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Jl. Raya ITS, Sukolilo, Surabaya, 60111, Indonesia; Department of Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mathematics, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Way Hui, Jati Agung, Lampung Selatan, 35365, Indonesia
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