基于物理信息神经网络的表面热流辨识

The Estimation of surface heat fluxes based on physics-informed neural network

  • 摘要: 辨识表面热流问题是一类典型的热传导逆问题。针对该问题,提出了一种基于物理信息神经网络(PINN)的表面热流辨识方法。该方法首先根据热传导问题构建满足输入输出的全连接神经网络,然后利用自动微分技术将一维热传导方程以残差形式融入神经网络的损失函数中作为物理知识约束,最后通过直接热传导问题提供的温度历程数据训练神经网络。当损失函数收敛到足够小,神经网络模型可近似热传导方程,进而使用神经网络模型辨识出表面热流。实验结果表明,基于PINN的表面热流辨识方法能有效地辨识得到表面热流,尤其在信息足够的条件下辨识结果令人满意,验证了方法的有效性。相比于传统辨识方法,PINN方法结合数据驱动和物理方程约束,辨识结果更优。在使用具有噪声数据训练模型时,可通过减小温度历程数据权重来提高模型的抗噪能力,说明了该方法能对噪声数据具有较好的鲁棒性。

     

    Abstract: The problem of estimating surface heat fluxes is a typical inverse heat conduction problem. To solve this problem, the estimation of surface heat fluxes based on physics-informed neural network(PINN) is proposed. Firstly, the fully connection neural network satisfying the heat conduction problem’s input and output is constructed. And then, the residual error of one-dimensional heat conduction equation is integrated into the loss function of the neural network as a physical knowledge constraint by using automatic differentiation technology. Finally, the neural network is trained by the temperature data provided by the direct heat conduction problem. When the loss function converges sufficiently small, the neural network model can approximate the heat conduction equation, and then the neural network model can be used to identify the surface heat flow. The results show that the estimation of surface heat flux based on PINN can effectively estimate the surface heat flux, especially under the condition of sufficient information, the results are satisfactory, which verifies the effectiveness of the method. Compared with conventional identification method, the PINN method integrates data-driven modeling with physical equation constraints, thereby achieving more accurate identification results. When using noisy data to train the model, the anti-noise ability of the model can be improved by reducing the weight of temperature data, the method based on PINN is robust to noisy data.

     

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