# Physics Informed Symbolic Networks

arXiv: https://arxiv.org/abs/2207.06240 · HTML: https://mlsanity.com/paper/2207.06240/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 12 of 12)

- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [Neural Arithmetic Logic Units](https://mlsanity.com/paper/1808.00508/) (2018)
- [HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks](https://mlsanity.com/paper/2111.01008/) (2021)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [Neural-Guided Symbolic Regression with Asymptotic Constraints](https://mlsanity.com/paper/1901.07714/) (2019)
- [Symbolically Solving Partial Differential Equations using Deep Learning](https://mlsanity.com/paper/2011.06673/) (2020)

## Built on by (most cited first, 3 of 3)

- [SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving](https://mlsanity.com/paper/2602.03816/) (2026)
- [DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement](https://mlsanity.com/paper/2609.00530/) (2026)
- [An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation](https://mlsanity.com/paper/2610.12003/) (2026)

## Abstract (arXiv)

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.