# Interpretable Scientific Discovery with Symbolic Regression: A Review

arXiv: https://arxiv.org/abs/2211.10873 · HTML: https://mlsanity.com/paper/2211.10873/

## Key facts

- Cited by 105 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 73 references that are in the map.
- First posted on arXiv 20 Nov 2022.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [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)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Learning Internal Representations (COLT 1995)](https://mlsanity.com/paper/1911.05781/) (2019)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Symbolic regression for scientific discovery: an application to wind speed forecasting](https://mlsanity.com/paper/2102.10570/) (2021)
- [Discovering State Variables Hidden in Experimental Data](https://mlsanity.com/paper/2112.10755/) (2021)
- [Improving Model-based Genetic Programming for Symbolic Regression of Small Expressions](https://mlsanity.com/paper/1904.02050/) (2019)

## Built on by (most cited first, 30 of 105)

- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [Predicting Ordinary Differential Equations with Transformers](https://mlsanity.com/paper/2307.12617/) (2023)
- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [Generative Discovery of Partial Differential Equations by Learning from Math Handbooks](https://mlsanity.com/paper/2505.05869/) (2025)
- [Comprehension Without Competence: Architectural Limits of LLMs in Symbolic Computation and Reasoning](https://mlsanity.com/paper/2507.10624/) (2025)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [SyMANTIC: An Efficient Symbolic Regression Method for Interpretable and Parsimonious Model Discovery in Science and Beyond](https://mlsanity.com/paper/2502.03367/) (2025)
- [A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programming](https://mlsanity.com/paper/2406.03585/) (2024)
- [Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks](https://mlsanity.com/paper/2501.11350/) (2025)
- [On the definition and importance of interpretability in scientific machine learning](https://mlsanity.com/paper/2505.13510/) (2025)
- [LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimization](https://mlsanity.com/paper/2602.10576/) (2026)
- [Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression](https://mlsanity.com/paper/2411.06833/) (2024)
- [Enabling Population-Level Parallelism in Tree-Based Genetic Programming for GPU Acceleration](https://mlsanity.com/paper/2501.17168/) (2025)
- [Scalable Neural Symbolic Regression using Control Variables](https://mlsanity.com/paper/2306.04718/) (2023)
- [Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients](https://mlsanity.com/paper/2401.04978/) (2024)
- [TorchSISSO: A PyTorch-Based Implementation of the Sure Independence Screening and Sparsifying Operator for Efficient and Interpretable Model Discovery](https://mlsanity.com/paper/2410.01752/) (2024)
- [Ab Initio Nonparametric Variable Selection for Scalable Symbolic Regression with Large p](https://mlsanity.com/paper/2410.13681/) (2024)
- [Forecasting VIX using interpretable Kolmogorov-Arnold networks](https://mlsanity.com/paper/2502.00980/) (2025)
- [DiSciPLE: Learning Interpretable Programs for Scientific Visual Discovery](https://mlsanity.com/paper/2502.10060/) (2025)
- [A Perspective on Symbolic Machine Learning in Physical Sciences](https://mlsanity.com/paper/2502.17993/) (2025)
- [SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discovery](https://mlsanity.com/paper/2506.06176/) (2025)
- [Iterated Agent for Symbolic Regression](https://mlsanity.com/paper/2510.08317/) (2025)

## Abstract (arXiv)

Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has recently gained a growing interest in deep learning as a data-driven model discovery method, achieving significant advances in various application domains ranging from fundamental to applied sciences. This survey presents a structured and comprehensive overview of symbolic regression methods and discusses their strengths and limitations.