论文标题
一种无监督/输出物理信息的卷积LSTM网络，用于使用Peridyanig差异操作员求解部分微分方程
An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator
论文作者
论文摘要
这项研究提出了一种新型的无监督卷积神经网络（NN）结构，该结构具有用于求解部分微分方程（PDE）的非局部相互作用。非局部性动力学差异操作员（PDDO）用作评估衍生物的卷积过滤器。 NN通过卷积长 - 短期内存（ConvlSTM）层在较小的潜在空间中捕获了较小的潜在空间中的时间范围。通过采用新颖的激活函数来改善与周期性行为的物理学学习体系结构的预测能力来修改ConvlSTM体系结构。在NN的输出和潜在的（减少）空间中以管理方程式的形式调用物理。通过考虑一些基准PDE，我们通过比较物理学知情的神经网络（PINN）类型求解器，证明了这种新型NN体系结构的训练性能和外推能力。与其他现有架构相比，它更有能力推断解决方案的未来时间段。
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning architecture for physics with periodic behavior. The physics is invoked in the form of governing equations at the output of the NN and in the latent (reduced) space. By considering a few benchmark PDEs, we demonstrate the training performance and extrapolation capability of this novel NN architecture by comparing against Physics Informed Neural Networks (PINN) type solvers. It is more capable of extrapolating the solution for future timesteps than the other existing architectures.
