  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.
