Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network

Wang Yahui; Xiao Hao; Ma Yu; Xie Yuchen; Chi Honghang

doi:10.13832/j.jnpe.2024.070062

Volume 46 Issue 2

Apr. 2025

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Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering, 2025, 46(2): 56-67. doi: 10.13832/j.jnpe.2024.070062

Citation:

Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering, 2025, 46(2): 56-67. doi: 10.13832/j.jnpe.2024.070062

Citation:

Wang Yahui, Xiao Hao, Ma Yu, Xie Yuchen, Chi Honghang. Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network[J]. Nuclear Power Engineering, 2025, 46(2): 56-67. doi: 10.13832/j.jnpe.2024.070062

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Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network

doi: 10.13832/j.jnpe.2024.070062

Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, Guangdong, 519082, China

Received Date: 2024-07-31
Rev Recd Date: 2024-08-21

Available Online: 2025-01-15

Publish Date: 2025-04-02

Abstract

Abstract

In order to improve the network reusability of the deep learning method and construct a deep network model suitable for different control equations and different physical parameters, a lattice Boltzmann method based on physical fusion neural network (PFNN-LBM) is proposed in this study. The unified discrete-velocity Boltzmann equation for equations with different characteristics is established under lattice Boltzmann method, and solved using the parameterize physics–informed neural network with a single network. The PFNN-LBM can simultaneously solve governing equations with different forms and different physical parameters within one single training. In order to test the accuracy and adaptability of PFNN-LBM, four types of macro-equations, including diffusion equation, nonlinear heat conduction equation, Sine-Gordon equation and Burgers-Fisher equation, are selected for prediction analysis. At the same time, the prediction performance under different physical parameters and the two-group neutron diffusion equations are tested. The calculation results show that the proposed PFNN-LBM can solve the control equations of different forms and different physical parameters with high accuracy after one training. This work can provide a novel framework for solving different types of equations efficiently and flexibly, and for engineering application, this work may have outstanding advantages in multi-physics coupling calculations.
- Physics-informed neural network,
- Lattice Boltzmann,
- Deep learning,
- Nonlinear convection-diffusion equations

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References(12)

References

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