# Generalizing the SINDy approach with nested neural networks

arXiv: https://arxiv.org/abs/2404.15742 · HTML: https://mlsanity.com/paper/2404.15742/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 59 references that are in the map.
- First posted on arXiv 24 Apr 2024.

## Builds on (most cited first, 30 of 36)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Improving exploration in policy gradient search: Application to symbolic optimization](https://mlsanity.com/paper/2107.09158/) (2021)
- [Symbolic regression outperforms other models for small data sets](https://mlsanity.com/paper/2103.15147/) (2021)
- [GSR: A Generalized Symbolic Regression Approach](https://mlsanity.com/paper/2205.15569/) (2022)
- [Priors for symbolic regression](https://mlsanity.com/paper/2304.06333/) (2023)
- [Discovering Mathematical Formulas from Data via GPT-guided Monte Carlo Tree Search](https://mlsanity.com/paper/2401.14424/) (2024)
- [Symbolic Visual Reinforcement Learning: A Scalable Framework with Object-Level Abstraction and Differentiable Expression Search](https://mlsanity.com/paper/2212.14849/) (2022)
- [A Transformer Model for Symbolic Regression towards Scientific Discovery](https://mlsanity.com/paper/2312.04070/) (2023)
- [Distilling Wikipedia mathematical knowledge into neural network models](https://mlsanity.com/paper/2104.05930/) (2021)
- [Incorporating domain knowledge into neural-guided search](https://mlsanity.com/paper/2107.09182/) (2021)
- [GFN-SR: Symbolic Regression with Generative Flow Networks](https://mlsanity.com/paper/2312.00396/) (2023)
- [Class Symbolic Regression: Gotta Fit 'Em All](https://mlsanity.com/paper/2312.01816/) (2023)

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

- [Discovering Governing Equations in the Presence of Uncertainty](https://mlsanity.com/paper/2507.09740/) (2025)
- [AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2604.18889/) (2026)

## Abstract (arXiv)

Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse regression to identify governing equations from data. This study introduces an enhanced method, Nested SINDy, that aims to increase the expressivity of the SINDy approach thanks to a nested structure. Indeed, traditional symbolic regression and system identification methods often fail with complex systems that cannot be easily described analytically. Nested SINDy builds on the SINDy framework by introducing additional layers before and after the core SINDy layer. This allows the method to identify symbolic representations for a wider range of systems, including those with compositions and products of functions. We demonstrate the ability of the Nested SINDy approach to accurately find symbolic expressions for simple systems, such as basic trigonometric functions, and sparse (false but accurate) analytical representations for more complex systems. Our results highlight Nested SINDy's potential as a tool for symbolic regression, surpassing the traditional SINDy approach in terms of expressivity. However, we also note the challenges in the optimization process for Nested SINDy and suggest future research directions, including the designing of a more robust methodology for the optimization process. This study proves that Nested SINDy can effectively discover symbolic representations of dynamical systems from data, offering new opportunities for understanding complex systems through data-driven methods.