论文标题
物理和数据共同驱动的替代建模方法,用于在不规则的几何域上预测温度场的预测
A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain
论文作者
论文摘要
在整个飞机结构优化环中,热分析起着非常重要的作用。但是,当直接应用传统的数值分析工具时,它会面临严重的计算负担,尤其是在每个优化涉及重复的参数修改和随后的热分析时。最近,随着深度学习的快速发展,已经引入了几种卷积神经网络(CNN)替代模型来克服这一障碍。但是,对于在不规则几何域(TFP-IGD)上的温度场预测,CNN几乎不能胜任,因为它们大多数源自加工常规图像。为了减轻这一困难,我们提出了一种新颖的物理和数据共同替代建模方法。首先,在将Bezier曲线适应几何参数化之后,引入了身体拟合的坐标映射,以在不规则的物理平面和常规计算平面之间产生坐标变换。其次,将具有部分微分方程(PDE)残留物作为损失函数的物理驱动的CNN替代物用于快速网格(Meshing Surnogate);然后,我们根据多级还原阶方法提出了一个数据驱动的替代模型,旨在在上述规则计算平面(热代理)中学习温度场解决方案。最后,将网络替代物提供的网格位置信息与热代替代物提供的标量温度场信息(合并模型)相结合,我们达到了从几何参数到不规则几何域的温度场预测的端到端替代模型。数值结果表明,与其他CNN方法相比,我们的方法可以显着提高较小数据集的精度预测,同时减少训练时间。
In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis followed. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.