Liu, Z.; Chen, Y.; Song, G.; Song, W.; Xu, J. Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics. Mathematics2023, 11, 4147.
Liu, Z.; Chen, Y.; Song, G.; Song, W.; Xu, J. Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics. Mathematics 2023, 11, 4147.
Liu, Z.; Chen, Y.; Song, G.; Song, W.; Xu, J. Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics. Mathematics2023, 11, 4147.
Liu, Z.; Chen, Y.; Song, G.; Song, W.; Xu, J. Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics. Mathematics 2023, 11, 4147.
Abstract
The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.
Copyright:
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