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SPH-PINN: An Improved Physics-Informed Neural Network Integrated with Smoothed Particle Hydrodynamics.

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Title: SPH-PINN: An Improved Physics-Informed Neural Network Integrated with Smoothed Particle Hydrodynamics.
Authors: Feng, Junxuan1 (AUTHOR), Rozi, Askar1 (AUTHOR), Imin, Rahmatjan1 (AUTHOR) rahmatjanim@xju.edu.cn
Source: International Journal of Computational Methods. Mar2026, Vol. 23 Issue 2, p1-23. 23p.
Subjects: Automatic differentiation, Particle methods (Numerical analysis), Partial differential equations, Finite difference method, Artificial neural networks, Computer simulation, Simulation methods & models, Deep learning
Abstract: In this paper, an integration of the improved smoothed particle hydrodynamics (SPH) method with physics-informed neural networks (PINNs) is presented. The improved SPH method is employed to replace automatic differentiation in computing the differential operators of the loss function within the neural network framework, facilitating accelerated neural network training and reducing computational time. Additionally, tests are conducted on two-dimensional partial differential equations (PDEs) and systems of PDEs, with comparisons made to the results obtained using automatic differentiation-based physics-informed neural network (AD-PINN) and finite difference-based physics-informed neural network (FD-PINN). The findings demonstrate that the proposed method achieves faster computation speeds, particularly when dealing with larger network layer sizes and increased equation complexity. It maintains errors within the same order of magnitude while avoiding nonphysical solutions. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Computational Methods is the property of World Scientific Publishing Company 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
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DbLabel: Engineering Source
An: 191379165
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  Data: SPH-PINN: An Improved Physics-Informed Neural Network Integrated with Smoothed Particle Hydrodynamics.
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  Data: <searchLink fieldCode="AR" term="%22Feng%2C+Junxuan%22">Feng, Junxuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Rozi%2C+Askar%22">Rozi, Askar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Imin%2C+Rahmatjan%22">Imin, Rahmatjan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rahmatjanim@xju.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Computational+Methods%22">International Journal of Computational Methods</searchLink>. Mar2026, Vol. 23 Issue 2, p1-23. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Automatic+differentiation%22">Automatic differentiation</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+methods+%28Numerical+analysis%29%22">Particle methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In this paper, an integration of the improved smoothed particle hydrodynamics (SPH) method with physics-informed neural networks (PINNs) is presented. The improved SPH method is employed to replace automatic differentiation in computing the differential operators of the loss function within the neural network framework, facilitating accelerated neural network training and reducing computational time. Additionally, tests are conducted on two-dimensional partial differential equations (PDEs) and systems of PDEs, with comparisons made to the results obtained using automatic differentiation-based physics-informed neural network (AD-PINN) and finite difference-based physics-informed neural network (FD-PINN). The findings demonstrate that the proposed method achieves faster computation speeds, particularly when dealing with larger network layer sizes and increased equation complexity. It maintains errors within the same order of magnitude while avoiding nonphysical solutions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Computational Methods is the property of World Scientific Publishing Company 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.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1142/S021987622550046X
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 23
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    Subjects:
      – SubjectFull: Automatic differentiation
        Type: general
      – SubjectFull: Particle methods (Numerical analysis)
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Finite difference method
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Simulation methods & models
        Type: general
      – SubjectFull: Deep learning
        Type: general
    Titles:
      – TitleFull: SPH-PINN: An Improved Physics-Informed Neural Network Integrated with Smoothed Particle Hydrodynamics.
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            NameFull: Feng, Junxuan
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            NameFull: Rozi, Askar
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            NameFull: Imin, Rahmatjan
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            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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            – TitleFull: International Journal of Computational Methods
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