论文标题
FITITENET：完全卷积的LSTM网络架构，用于时间相关的部分微分方程
FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations
论文作者
论文摘要
在这项工作中，我们提出了一种机器学习方法，用于减少数值求解时间相关的偏微分方程（PDE）时的错误。我们使用完全卷积的LSTM网络来利用PDES的时空动力学。神经网络可增强通常用于求解PDE的有限差异和有限体积方法（FDM/FVM），从而使我们能够根据方法的收敛顺序保持保证。我们在模拟数据上训练网络，并表明与基线算法相比，我们的网络可以将误差减少2至3倍。我们在三个PDE上演示了我们的方法，每个PDE都有定性不同的动态。我们查看线性对流方程，该方程以恒定的速度传播其初始条件，Inviscid Burgers的方程会产生冲击波，而Kuramoto-Sivashinskin（KS）方程式是混乱的。
In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of PDEs. The neural network serves to enhance finite-difference and finite-volume methods (FDM/FVM) that are commonly used to solve PDEs, allowing us to maintain guarantees on the order of convergence of our method. We train the network on simulation data, and show that our network can reduce error by a factor of 2 to 3 compared to the baseline algorithms. We demonstrate our method on three PDEs that each feature qualitatively different dynamics. We look at the linear advection equation, which propagates its initial conditions at a constant speed, the inviscid Burgers' equation, which develops shockwaves, and the Kuramoto-Sivashinsky (KS) equation, which is chaotic.
