# Symbolic Regression via Neural Networks

arXiv: https://arxiv.org/abs/2605.04337 · HTML: https://mlsanity.com/paper/2605.04337/

## Key facts

- Cited by 2 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 5 May 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regression](https://mlsanity.com/paper/2008.07281/) (2020)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)
- [How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification](https://mlsanity.com/paper/1905.08061/) (2019)

## Built on by (most cited first, 2 of 2)

- [Symbolic Neural ODEs: Learning interpretable models from time-series data](https://mlsanity.com/paper/2608.22112/) (2026)
- [Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis](https://mlsanity.com/paper/2609.04329/) (2026)

## Abstract (arXiv)

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model, then show the accuracy of our algorithm across a range of classical dynamical systems.