基于物理信息神经网络的气动数据融合方法

Aerodynamic data fusion method based on physics-informed neural network

为了解决训练传统深度神经网络对大数据的依赖问题,气动数据中包含的物理结构信息需要被充分利用。物理信息神经网络(physics-informed neural network,PINN)是一种非监督的学习算法,采用深度神经网络直接逼近流场偏微分方程的解,因此适用于气动数据的建模。然而训练PINN时,损失函数反映的是抽样点处神经网络所拟合的偏微分方程值的偏差,对于复杂的非线性偏微分方程,这一偏差不能准确反映神经网络所拟合的函数与微分方程解函数的偏差,而且用神经网络拟合初始条件和边界条件时,不可避免存在拟合误差,误差随空间和时间累计,这使PINN的建模精度相比传统的模型没有优势。为了解决这些问题,本文把PINN与流场的计算流体动力学(Computational Fluid Dynamics,CFD)仿真结果进行融合,在流场抽样点处的损失函数中增加了PINN在该点的输出与流场在该点的CFD值偏差,从而提高了神经网络的建模精度。根据CFD仿真时使用的模型,融合方式采用瞬时模式或时均模式。测试结果表明该方法能够有效提高PINN的建模精度。

To solve the issue that conventional deep neural networks(DNN)needs prohibitively vast amount of data,the structure information contained in aerodynamic data needs to be fully utilized.Physics-informed neural network(PINN)is an unsupervised learning algorithm that uses deep neural networks to directly approximate solutions to partial differential equations(PDEs)of the flow fields,thus suitable for modeling aerodynamic problems.However,during the training process of PINN,the loss function only depicts the deviation of PDE at the training sample points,and for complex nonlinear partial differential equations,this deviation cannot accurately reflect the error between the function fitted by neural networks and the solution of PDEs.Moreover,errors inevitably exist in the boundary and initial conditions when fitted with neural networks,which accumulate in space and time,making the modeling accuracy of PINN less favorable compared to traditional models.In order to address the above issue,the present study integrates PINN with computational fluid dynamics(CFD)simulation results of the flow fields,which adds the deviation between PINN output and CFD value in the loss function at sampling points of the flow field,thus improving the modeling accuracy of the neural network. According to the model used in CFD simulations, the fusion mode can adopt instantaneous mode or time-averaged mode. Experimental results suggest that the proposed method can effectively improve the modeling accuracy of PINN.