A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations

Endah R.M. Putri*, Muhammad L. Shahab, Mohammad Iqbal, Imam Mukhlash, Amirul Hakam, Lutfi Mardianto, Hadi Susanto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)120-127
Number of pages8
JournalComputers and Mathematics with Applications
Volume154
DOIs
Publication statusPublished - 15 Jan 2024

Keywords

  • Backward stochastic differential equation
  • Genetic algorithm
  • High dimensionality
  • Nonlinear equations

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