# Neural-Network-Directed Genetic Programmer for Discovery of Governing Equations

arXiv: https://arxiv.org/abs/2203.08808 · HTML: https://mlsanity.com/paper/2203.08808/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [A Novel Neural Network-Based Symbolic Regression Method: Neuro-Encoded Expression Programming](https://mlsanity.com/paper/1904.03368/) (2019)

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

- [GSR: A Generalized Symbolic Regression Approach](https://mlsanity.com/paper/2205.15569/) (2022)
- [Symbolic Regression via Control Variable Genetic Programming](https://mlsanity.com/paper/2306.08057/) (2023)
- [Racing Control Variable Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2309.07934/) (2023)

## Abstract (arXiv)

We develop a symbolic regression framework for extracting the governing mathematical expressions from observed data. The evolutionary approach, faiGP, is designed to leverage the properties of a function algebra that have been encoded into a grammar, providing a theoretical guarantee of universal approximation and a way to minimize bloat. In this framework, the choice of operators of the grammar may be informed by a physical theory or symmetry considerations. Since there is currently no theory that can derive the 'constants of nature', an empirical investigation on extracting these coefficients from an evolutionary process is of methodological interest. We quantify the impact of different types of regularizers, including a diversity metric adapted from studies of the transcriptome and a complexity measure, on the performance of the framework. Our implementation, which leverages neural networks and a genetic programmer, generates non-trivial symbolically equivalent expressions ("Ramanujan expressions") or approximations with potentially interesting numerical applications. To illustrate the framework, a model of ligand-receptor binding kinetics, including an account of gene regulation by transcription factors, and a model of the regulatory range of the cistrome from omics data are presented. This study has important implications on the development of data-driven methodologies for the discovery of governing equations in experimental data derived from new sensing systems and high-throughput screening technologies.