A Deep Genetic Algorithm (Deep-Ga) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations

15 Pages Posted: 17 Feb 2022

See all articles by Endah Putri

Endah Putri

Institut Teknologi Sepuluh Nopember

Muhammad Luthfi Shahab

Institute of Technology Sepuluh Nopember (ITS)

Mohammad Iqbal

Institut Teknologi Sepuluh Nopember

Imam Mukhlash

Institut Teknologi Sepuluh Nopember

amir hakam

Institut Teknologi Sepuluh Nopember

Lutfi Mardianto

Institut Teknologi Sumatera

Hadi Susanto

Khalifa University

Abstract

Solving non-linear parabolic partial differential equations (PDEs) in high dimension becomes an interest for its curse of dimensionality problem. Recently, a deep learning method associated with a backward stochastic differential equation (deep-BSDE) to solve the PDEs draws intensive discussions for its remarkable results. In this paper we propose an alternative, namely the deep-GA method, to improve the performance of the former method. We embed the genetic algorithm (GA) into the BSDE solver to optimize the initial guess that results in a more efficient computation with higher accuracy. Our proposed method is applied to two nonlinear parabolic PDEs, i.e., the Black-Scholes equation with default risk and Hamilton-Jacobi-Bellman equation. We compare the results of our method to the deep-BSDE and show that our method provides a better accuracy and efficiency than the deep-BSDE.

Keywords: high dimensionality, non-linear equations, Genetic algorithm, backward stochastic differential equation

Suggested Citation

Putri, Endah and Shahab, Muhammad Luthfi and Iqbal, Mohammad and Mukhlash, Imam and hakam, amir and Mardianto, Lutfi and Susanto, Hadi, A Deep Genetic Algorithm (Deep-Ga) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations. Available at SSRN: https://ssrn.com/abstract=4028968 or http://dx.doi.org/10.2139/ssrn.4028968

Endah Putri (Contact Author)

Institut Teknologi Sepuluh Nopember ( email )

Muhammad Luthfi Shahab

Institute of Technology Sepuluh Nopember (ITS) ( email )

Jalan Mulyorejo Tengah No. 69
Surabaya, ID East Java 60111
Indonesia

Mohammad Iqbal

Institut Teknologi Sepuluh Nopember ( email )

Surabaya, 60111
Indonesia

Imam Mukhlash

Institut Teknologi Sepuluh Nopember ( email )

Surabaya, 60111
Indonesia

Amir Hakam

Institut Teknologi Sepuluh Nopember ( email )

Lutfi Mardianto

Institut Teknologi Sumatera ( email )

Jalan Terusan Ryacudu, Way Hui, Jati Agung
Way Huwi, Jati Agung
Kabupaten Lampung Selatan, 35365
Indonesia

Hadi Susanto

Khalifa University ( email )

Abu Dhabi
United Arab Emirates

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