物理信息神经网络与单松弛时间格子玻尔兹曼方法相结合解决流体力学反问题,Mathematics

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物理信息神经网络与单松弛时间格子玻尔兹曼方法相结合解决流体力学反问题
Mathematics ( IF 2.3 ) Pub Date : 2023-10-01 , DOI: 10.3390/math11194147
Zhixiang Liu ₁ , Yuanji Chen ₁ , Ge Song ₁ , Wei Song ₁ , Jingxiang Xu ₂

Affiliation

物理信息神经网络（PINN）通过将物理原理与神经网络算法相结合，提高数据利用效率，从而确保其预测与物理定律一致且稳定。PINN 开辟了解决流体力学逆问题的新方法。基于单弛豫时间格子玻尔兹曼方法（SRT-LBM）和 Bhatnagar-Gross-Krook（BGK）碰撞算子，本文提出了 PINN-SRT-LBM 模型来求解流体力学逆问题。PINN-SRT-LBM 模型由三个部分组成。第一个组件涉及一个深度神经网络，用于预测 SRT-LBM 内不同离散速度方向的平衡控制方程。第二个组件采用另一个深度神经网络来预测非平衡控制方程，能够推断流体的非平衡特性。第三个组件是物理信息函数，它将前两个网络的输出转换为物理信息。通过最小化物理偏微分方程 (PDE) 的残差，物理信息函数可以推断出相关的流动宏观量。该模型根据物理信息函数的构造演化出两个适用于不同维度的子模型，分别命名为PINN-SRT-LBM-I和PINN-SRT-LBM-II模型。这项工作的创新之处在于通过解释函数将SRT-LBM和离散速度模型作为物理驱动器引入到神经网络中。所以，PINN-SRT-LBM 允许给定的神经网络处理各种维度的逆问题并专注于特定问题的解决。我们的实验结果证实了该模型对计算域内不同雷诺数下的流量信息的准确预测。依靠PINN-SRT-LBM模型，可以有效地解决流体力学中的反问题。

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Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics

Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws. PINNs open 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 equilibrium control equations in different discrete velocity directions within the SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling the 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 information. 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 that are applicable to different dimensions, named the PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physics-informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into a neural network through the interpretation function. Therefore, the PINN-SRT-LBM allows a given neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Our experimental results confirm the accurate prediction by this model of flow information at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

更新日期：2023-10-01

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