论文标题
使用空间和内存意识到深度学习的参数化时间相关PDE的订单建模减少
Reduced Order Modeling for Parameterized Time-Dependent PDEs using Spatially and Memory Aware Deep Learning
论文作者
论文摘要
我们为基于现代学习的参数化时间依赖性PDE提供了一种新颖的减少订单模型（ROM）方法。 ROM适用于多Query问题，并且是无引人注目的。它分为两个不同的阶段：基于卷积自动编码器的空间分布的自由度，以及基于内存意识到的神经网络（NNS），特别是因果卷积和较长的短期记忆NN，可以根据卷积自动编码器的空间自由度处理空间分布的自由度。讨论了确保概括和稳定性的策略。该方法在热方程，对流方程和不可压缩的Navier-Stokes方程上进行了测试，以显示ROM可以处理的各种问题。
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear dimensionality reduction stage that handles the spatially distributed degrees of freedom based on convolutional autoencoders, and a parameterized time-stepping stage based on memory aware neural networks (NNs), specifically causal convolutional and long short-term memory NNs. Strategies to ensure generalization and stability are discussed. The methodology is tested on the heat equation, advection equation, and the incompressible Navier-Stokes equations, to show the variety of problems the ROM can handle.
