Physics Informed Symbolic Networks
Abstract
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.
Cite
@article{arxiv.2207.06240,
title = {Physics Informed Symbolic Networks},
author = {Ritam Majumdar and Vishal Jadhav and Anirudh Deodhar and Shirish Karande and Lovekesh Vig and Venkataramana Runkana},
journal= {arXiv preprint arXiv:2207.06240},
year = {2022}
}
Comments
Neural Information Processing Systems 2022: The Symbiosis of Deep Learning and Differential Equations Workshop