论文标题
物理知情符号网络
Physics Informed Symbolic Networks
论文作者
论文摘要
我们介绍了物理知情的符号网络（PISN），该网络利用物理信息损失来获得偏微分方程系统（PDE）系统的符号解决方案。给定无上下文的语法来描述符号表达式的语言，我们建议将加权总和作为选择生产规则的连续近似。我们使用此近似来定义多层符号网络。我们考虑Kovasznay流（Navier-Stokes）和二维粘性汉堡的方程式，以说明PISN能够提供与各种启动前进进步的PINN相当的性能：多个输出和管理方程，域名，域名组合，超网络。此外，我们建议使用多层感知器（MLP）操作员对符号网络的残基进行建模。观察到PINSN比标准PINN给出2-3个性能增长顺序。
We introduce Physics Informed Symbolic Networks (PISN) which utilize physics-informed loss to obtain a symbolic solution for a system of Partial Differential Equations (PDE). Given a context-free grammar to describe the language of symbolic expressions, we propose to use weighted sum as continuous approximation for selection of a production rule. We use this approximation to define multilayer symbolic networks. We consider Kovasznay flow (Navier-Stokes) and two-dimensional viscous Burger's equations to illustrate that PISN are able to provide a performance comparable to PINNs across various start-of-the-art advances: multiple outputs and governing equations, domain-decomposition, hypernetworks. Furthermore, we propose Physics-informed Neurosymbolic Networks (PINSN) which employ a multilayer perceptron (MLP) operator to model the residue of symbolic networks. PINSNs are observed to give 2-3 orders of performance gain over standard PINN.
