多重进化深度神经网络（Multi-EDNN）
Multi evolutional deep neural networks (Multi-EDNN)
AI总结：
针对单一网络求解大规模耦合PDE计算成本高的问题，提出Multi-EDNN方法，通过C-EDNN和D-EDNN分别实现变量解耦与空间分区，在典型问题上验证了其有效性。
摘要：
进化深度神经网络（EDNN）通过使用控制方程推进解场的网络表示来求解偏微分方程（PDE）。使用单一网络在大型域上求解耦合PDE需要大量的网络参数，并产生显著的计算成本。我们引入了耦合EDNN（C-EDNN）来求解PDE系统，该方法为每个状态变量使用独立的网络，这些网络仅通过控制方程耦合。我们还引入了分布式EDNN（D-EDNN），通过将全局域空间划分为多个单元，并为每个单元分配独立的EDNN来求解PDE的局部演化。然后，网络在其界面处交换解和通量，类似于通量重构方法，并确保PDE动力学在相邻单元之间被准确保持。C-EDNN和D-EDNN共同构成了Multi-EDNN方法的通用类别。我们借助典型问题演示了这些方法，包括线性平流、热方程以及库埃特流和泰勒-格林流中的可压缩纳维-斯托克斯方程。
英文摘要：
Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains requires a large number of network parameters and incurs a significant computational cost. We introduce coupled EDNN (C-EDNN) to solve systems of PDEs by using independent networks for each state variable, which are only coupled through the governing equations. We also introduce distributed EDNN (D-EDNN) by spatially partitioning the global domain into several elements and assigning individual EDNNs to each element to solve the local evolution of the PDE. The networks then exchange the solution and fluxes at their interfaces, similar to flux-reconstruction methods, and ensure that the PDE dynamics are accurately preserved between neighboring elements. Together C-EDNN and D-EDNN form the general class of Multi-EDNN methods. We demonstrate these methods with aid of canonical problems including linear advection, the heat equation, and the compressible Navier-Stokes equations in Couette and Taylor-Green flows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
