# ERBench: A Benchmark and Testsuite for Equation Discovery Algorithms

arXiv: https://arxiv.org/abs/2606.09276 · HTML: https://mlsanity.com/paper/2606.09276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 65 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [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)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (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)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [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)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert](https://mlsanity.com/paper/2308.09474/) (2023)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [PhysGym: Benchmarking LLMs in Interactive Physics Discovery with Controlled Priors](https://mlsanity.com/paper/2507.15550/) (2025)
- [MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task](https://mlsanity.com/paper/2402.18603/) (2024)
- [A Transformer Model for Symbolic Regression towards Scientific Discovery](https://mlsanity.com/paper/2312.04070/) (2023)
- [SyMANTIC: An Efficient Symbolic Regression Method for Interpretable and Parsimonious Model Discovery in Science and Beyond](https://mlsanity.com/paper/2502.03367/) (2025)
- [AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge](https://mlsanity.com/paper/2504.01538/) (2025)
- [Scaling Up Unbiased Search-based Symbolic Regression](https://mlsanity.com/paper/2506.19626/) (2025)

## Abstract (arXiv)

Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data. Technically, equation discovery is implemented by symbolic regression algorithms. Performance of symbolic regression for equation discovery is measured along two dimensions: Prediction accuracy on test data, and recovery of known groundtruth formulas. For standard regression, accuracy is typically measured on in-domain test data, for instance, by splitting a data set randomly into training and test data. While this makes sense for in-domain interpolation, which is the common goal in ordinary regression, it can be a misleading proxy for true model discovery and generalization. The obvious alternative is to measure out-of-domain accuracy. However, obtaining challenging out-of-domain test data is a non-trivial problem. Therefore, we focus on equation recovery for evaluating symbolic regression algorithms for equation discovery. The rationale is that symbolic regression algorithms that perform well in recovering known groundtruth formulas are good candidates to perform well in unknown equation discovery. Existing benchmarks for symbolic regression include equation recovery tasks, however, with only a small number of groundtruth formulas that are publicly known. Moreover, these benchmarks place less emphasis on evaluating the robustness of algorithms in terms of their behavior under changing dimensionality, sampling size, sampling distribution and sampling domain. This, however, is of central importance to practitioners wanting to discover equations for modeling natural phenomena, since data is almost certainly noisy and comes from diverse domains, distributions, and sample sizes. To fill this gap, we introduce the Equation Recovery Benchmark (ERBench), a new evaluation framework designed to rigorously assess algorithms explicitly targeting the task of equation discovery.