论文标题
神经基础功能，用于加速溶液到高音欧拉方程
Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations
论文作者
论文摘要
我们提出了一种使用一组我们称为神经基础功能（NBF）的神经网络来解决部分微分方程（PDE）的方法。这个NBF框架是POD DeepOnet操作方法的一种新颖的变化，我们将一组神经网络回归到降低的订单正交分解（POD）基础上。然后将这些网络与分支网络结合使用，该网络摄入规定的PDE的参数以计算降低的订单近似值。该方法应用于高速流条件条件的稳态EULER方程（Mach 10-30），在该方程中，我们考虑了围绕圆柱体的2D流，从而形成了冲击条件。然后，我们将NBF预测用作高保真计算流体动力学（CFD）求解器（CFD ++）的初始条件，以显示更快的收敛性。还将提供用于培训和实施该算法的经验教训。
We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where we regress a set of neural networks onto a reduced order Proper Orthogonal Decomposition (POD) basis. These networks are then used in combination with a branch network that ingests the parameters of the prescribed PDE to compute a reduced order approximation to the PDE. This approach is applied to the steady state Euler equations for high speed flow conditions (mach 10-30) where we consider the 2D flow around a cylinder which develops a shock condition. We then use the NBF predictions as initial conditions to a high fidelity Computational Fluid Dynamics (CFD) solver (CFD++) to show faster convergence. Lessons learned for training and implementing this algorithm will be presented as well.
