# Genetic Programming Based Symbolic Regression for Analytical Solutions to Differential Equations

arXiv: https://arxiv.org/abs/2302.03175 · HTML: https://mlsanity.com/paper/2302.03175/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 1 of 1)

- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)

## Built on by (most cited first, 6 of 6)

- [Interpreting and generalizing deep learning in physics-based problems with functional linear models](https://mlsanity.com/paper/2307.04569/) (2023)
- [Closed-form Solutions: A New Perspective on Solving Differential Equations](https://mlsanity.com/paper/2405.14620/) (2024)
- [Identifying Unknown Stochastic Dynamics via Finite expression methods](https://mlsanity.com/paper/2504.07085/) (2025)
- [Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams](https://mlsanity.com/paper/2509.21355/) (2025)
- [Fundamentals of Regression](https://mlsanity.com/paper/2512.01920/) (2025)
- [DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement](https://mlsanity.com/paper/2609.00530/) (2026)

## Abstract (arXiv)

In this paper, we present a machine learning method for the discovery of analytic solutions to differential equations. The method utilizes an inherently interpretable algorithm, genetic programming based symbolic regression. Unlike conventional accuracy measures in machine learning we demonstrate the ability to recover true analytic solutions, as opposed to a numerical approximation. The method is verified by assessing its ability to recover known analytic solutions for two separate differential equations. The developed method is compared to a conventional, purely data-driven genetic programming based symbolic regression algorithm. The reliability of successful evolution of the true solution, or an algebraic equivalent, is demonstrated.