## Details

Original language | English |
---|---|

Pages (from-to) | 303-317 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 143 |

Early online date | 30 May 2023 |

Publication status | Published - 1 Aug 2023 |

## Abstract

We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

## Keywords

- Boundary layer flow, Deep learning, Hyper-parameter optimization, Melting heat transfer, Physics-informed neural networks, Sensitivity analysis, Sisko fluid, Transfer learning

## ASJC Scopus subject areas

- Mathematics(all)
**Modelling and Simulation**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**

## Cite this

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- Harvard
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- BibTeX
- RIS

**Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning.**/ Guo, Hongwei; Zhuang, Xiaoying; Alajlan, Naif et al.

In: Computers and Mathematics with Applications, Vol. 143, 01.08.2023, p. 303-317.

Research output: Contribution to journal › Article › Research › peer review

*Computers and Mathematics with Applications*, vol. 143, pp. 303-317. https://doi.org/10.1016/j.camwa.2023.05.014

*Computers and Mathematics with Applications*,

*143*, 303-317. https://doi.org/10.1016/j.camwa.2023.05.014

}

TY - JOUR

T1 - Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning

AU - Guo, Hongwei

AU - Zhuang, Xiaoying

AU - Alajlan, Naif

AU - Rabczuk, Timon

PY - 2023/8/1

Y1 - 2023/8/1

N2 - We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

AB - We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

KW - Boundary layer flow

KW - Deep learning

KW - Hyper-parameter optimization

KW - Melting heat transfer

KW - Physics-informed neural networks

KW - Sensitivity analysis

KW - Sisko fluid

KW - Transfer learning

UR - http://www.scopus.com/inward/record.url?scp=85160574879&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2023.05.014

DO - 10.1016/j.camwa.2023.05.014

M3 - Article

AN - SCOPUS:85160574879

VL - 143

SP - 303

EP - 317

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -