论文标题
重新访问PINN：生成的对抗物理学的神经网络和点加权方法
Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method
论文作者
论文摘要
物理知识的神经网络（PINN）为求解部分微分方程（PDE）提供了一个深度学习框架，并已广泛用于各种PDE问题。但是，在PINN的应用中仍然存在一些挑战：1）PINN的机制不合适（至少不能直接应用）来利用少量（通常很少）额外的信息样本来完善网络； 2）对于某些复杂的PDE，训练Pinn的效率通常会变得较低。在本文中，我们提出了生成的对抗物理信息信息的神经网络（GA-PINN），该神经网络（GA-PINN）将生成的对抗（GA）机制与PINNS结构相结合，以通过仅利用对PDES的小尺寸的精确解决方案来提高PINN的性能。受Adaboost方法的加权策略的启发，我们引入了一种点加权方法（PW）方法，以提高PINN的训练效率，在每个训练迭代时，每个样本点的权重都会自适应更新。数值实验表明，Ga-pinns在许多众所周知的PDE中的表现都优于PINN，并且PW方法还提高了训练Pinn和Ga-Pinn的效率。
Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable (at least cannot be directly applied) to exploiting a small size of (usually very few) extra informative samples to refine the networks; and 2) the efficiency of training PINNs often becomes low for some complicated PDEs. In this paper, we propose the generative adversarial physics-informed neural network (GA-PINN), which integrates the generative adversarial (GA) mechanism with the structure of PINNs, to improve the performance of PINNs by exploiting only a small size of exact solutions to the PDEs. Inspired from the weighting strategy of the Adaboost method, we then introduce a point-weighting (PW) method to improve the training efficiency of PINNs, where the weight of each sample point is adaptively updated at each training iteration. The numerical experiments show that GA-PINNs outperform PINNs in many well-known PDEs and the PW method also improves the efficiency of training PINNs and GA-PINNs.
