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.
翻译:我们引入了物理知情符号网络(PISN ), 利用物理知情损失为局部差异方程式(PDE ) 获得象征性的解决方案。 鉴于用于描述符号表达语言的无上下文语法, 我们提议使用加权和连续近似值作为选择生产规则的连续近似值。 我们使用这一近似值来定义多层符号网络。 我们考虑 Kovasznay 流(Navier-Stokes) 和二维对流 Burger 等式, 以说明 PISN 能够提供与PINN 相近的性能, 跨越各种艺术初始进步: 多重输出和治理方程式、 域分解、 超网络。 此外, 我们提议使用多层感应(MLP) 操作器来模拟符号网络的残渣。 PINN 观察到PINN 能够在标准的PINN 上提供2-3级性绩效增益令。