论文标题
Deqgan：学习具有生成对抗网络的Pinn的损失功能
DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks
论文作者
论文摘要
微分方程的解决方案具有重要的科学和工程意义。物理知识的神经网络（PINN）已成为解决微分方程的有前途方法，但它们缺乏使用任何特定损失函数的理论理由。这项工作提出了微分方程gan（Deqgan），这是一种使用生成对抗网络来求解微分方程的新方法，以“学习损失函数”以优化神经网络。在一个十二个普通和部分微分方程的套件上呈现结果，包括非线性汉堡，艾伦·卡恩，汉密尔顿和改良的爱因斯坦的重力方程，我们表明，deqgan可以比使用$ l_2 $ l_2 $，$ l_1 $ $ l_1 $ and Huber and Huber and Huber and Huber Loffions的PINN低多个均值误差。我们还表明，Deqgan实现了具有流行数值方法竞争的解决方案精确度。最后，我们提出了两种方法，以提高Deqgan对不同的高参数设置的鲁棒性。
Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving differential equations, but they lack a theoretical justification for the use of any particular loss function. This work presents Differential Equation GAN (DEQGAN), a novel method for solving differential equations using generative adversarial networks to "learn the loss function" for optimizing the neural network. Presenting results on a suite of twelve ordinary and partial differential equations, including the nonlinear Burgers', Allen-Cahn, Hamilton, and modified Einstein's gravity equations, we show that DEQGAN can obtain multiple orders of magnitude lower mean squared errors than PINNs that use $L_2$, $L_1$, and Huber loss functions. We also show that DEQGAN achieves solution accuracies that are competitive with popular numerical methods. Finally, we present two methods to improve the robustness of DEQGAN to different hyperparameter settings.
