View in EDS

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

Saved in:
Bibliographic Details
Title: A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations.
Authors: Putri, Endah R.M.1 (AUTHOR) endahrmp@matematika.its.ac.id, Shahab, Muhammad L.1,2 (AUTHOR), Iqbal, Mohammad1 (AUTHOR), Mukhlash, Imam1 (AUTHOR), Hakam, Amirul1 (AUTHOR), Mardianto, Lutfi3 (AUTHOR), Susanto, Hadi2 (AUTHOR)
Source: Computers & Mathematics with Applications. Jan2024, Vol. 154, p120-127. 8p.
Subjects: Parabolic differential equations, Stochastic differential equations, Hamilton-Jacobi-Bellman equation, Machine learning, Partial differential equations, Genetic algorithms
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. • We introduce a deep-GA method. • The method provides a better accuracy and efficiency than the deep-BSDE solver. • Efficiency and accuracy is obtained by embedding a genetic algorithm (GA). • We solve the Black-Scholes with default risk and Hamilton-Jacobi-Bellman equations. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 174529399
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Putri%2C+Endah+R%2EM%2E%22">Putri, Endah R.M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> endahrmp@matematika.its.ac.id</i><br /><searchLink fieldCode="AR" term="%22Shahab%2C+Muhammad+L%2E%22">Shahab, Muhammad L.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Iqbal%2C+Mohammad%22">Iqbal, Mohammad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mukhlash%2C+Imam%22">Mukhlash, Imam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hakam%2C+Amirul%22">Hakam, Amirul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mardianto%2C+Lutfi%22">Mardianto, Lutfi</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Susanto%2C+Hadi%22">Susanto, Hadi</searchLink><relatesTo>2</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Jan2024, Vol. 154, p120-127. 8p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Parabolic+differential+equations%22">Parabolic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+differential+equations%22">Stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi-Bellman+equation%22">Hamilton-Jacobi-Bellman equation</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Genetic+algorithms%22">Genetic algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. • We introduce a deep-GA method. • The method provides a better accuracy and efficiency than the deep-BSDE solver. • Efficiency and accuracy is obtained by embedding a genetic algorithm (GA). • We solve the Black-Scholes with default risk and Hamilton-Jacobi-Bellman equations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=174529399
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.camwa.2023.11.022
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 8
        StartPage: 120
    Subjects:
      – SubjectFull: Parabolic differential equations
        Type: general
      – SubjectFull: Stochastic differential equations
        Type: general
      – SubjectFull: Hamilton-Jacobi-Bellman equation
        Type: general
      – SubjectFull: Machine learning
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Genetic algorithms
        Type: general
    Titles:
      – TitleFull: A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Putri, Endah R.M.
      – PersonEntity:
          Name:
            NameFull: Shahab, Muhammad L.
      – PersonEntity:
          Name:
            NameFull: Iqbal, Mohammad
      – PersonEntity:
          Name:
            NameFull: Mukhlash, Imam
      – PersonEntity:
          Name:
            NameFull: Hakam, Amirul
      – PersonEntity:
          Name:
            NameFull: Mardianto, Lutfi
      – PersonEntity:
          Name:
            NameFull: Susanto, Hadi
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 15
              M: 01
              Text: Jan2024
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-print
              Value: 08981221
          Numbering:
            – Type: volume
              Value: 154
          Titles:
            – TitleFull: Computers & Mathematics with Applications
              Type: main
ResultId 1