论文标题
通过生成对抗网络对微分方程的解决方案的无监督学习
Unsupervised Learning of Solutions to Differential Equations 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。最近，人们对通过神经网络解决微分方程的兴趣越来越大。这项工作开发了一种新的方法，可以使用无监督的神经网络求解微分方程，该方程将生成性对抗网络（GAN）应用于\ emph {学习损失函数}以优化神经网络。我们提出的经验结果表明，我们称之为微分方程gan（Deqgan）的方法比基于（平方）$ l_2 $，$ l_1 $和HUBER损失功能的替代无监督神经网络方法的均方形误差要低多个数量级。此外，我们表明Deqgan可以实现与传统数值方法竞争的解决方案精度。最后，我们分析了方法的稳定性，并发现它对我们在附录中提供的超参数的选择敏感。 可在https://github.com/dylanrandle/denn上找到代码。请向[email protected]致辞。
Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving differential equations with unsupervised neural networks that applies Generative Adversarial Networks (GANs) to \emph{learn the loss function} for optimizing the neural network. We present empirical results showing that our method, which we call Differential Equation GAN (DEQGAN), can obtain multiple orders of magnitude lower mean squared errors than an alternative unsupervised neural network method based on (squared) $L_2$, $L_1$, and Huber loss functions. Moreover, we show that DEQGAN achieves solution accuracy that is competitive with traditional numerical methods. Finally, we analyze the stability of our approach and find it to be sensitive to the selection of hyperparameters, which we provide in the appendix. Code available at https://github.com/dylanrandle/denn. Please address any electronic correspondence to [email protected].
