# Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees

arXiv: https://arxiv.org/abs/2411.00011 · HTML: https://mlsanity.com/paper/2411.00011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programming](https://mlsanity.com/paper/2406.03585/) (2024)
- [Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus](https://mlsanity.com/paper/2310.06609/) (2023)

## Built on by (most cited first, 1 of 1)

- [Searching the Space of Feed-Forward Neural-Network Weight-Update Rules with Fixed Depth Symbolic Regression](https://mlsanity.com/paper/2607.21855/) (2026)

## Abstract (arXiv)

This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and boundary conditions, demonstrating its accuracy and ability to find approximate solutions efficiently. This framework offers a promising, scalable solution for finding approximate solutions to differential equations, with the potential for future improvements in computational performance and applicability to more complex systems involving vector-valued objectives.