ERBench: New Benchmark Framework for Evaluating Equation Discovery Algorithms
Researchers have introduced ERBench, a new evaluation framework designed to more rigorously assess symbolic regression algorithms used in scientific equation discovery. Existing benchmarks for symbolic regression contain only a small number of ground-truth formulas and inadequately test algorithm robustness across varying data conditions such as noise, dimensionality, sample size, and sampling distribution. ERBench addresses this gap, which matters because more reliable benchmarking could accelerate the identification of trustworthy algorithms for discovering mathematical models of natural phenomena.
A preprint submitted to arXiv on June 8, 2026 introduces ERBench, a benchmark and test suite aimed at more comprehensively evaluating symbolic regression algorithms in the context of equation discovery. Equation discovery seeks to automate the derivation of scientific models as mathematical equations directly from data, and symbolic regression is the primary technical approach used to achieve this. The authors argue that standard accuracy metrics based on in-domain test data are a misleading proxy for true model discovery, since real-world scientific data is noisy and spans diverse domains, distributions, and sample sizes. While existing benchmarks do include equation recovery tasks, they rely on a limited set of publicly known ground-truth formulas and do not sufficiently probe algorithm robustness under changing conditions. ERBench focuses specifically on equation recovery—testing whether algorithms can reconstruct known ground-truth formulas—as a principled proxy for performance on unknown equation discovery tasks. The framework is designed to systematically vary dimensionality, sampling size, sampling distribution, and sampling domain to stress-test algorithm behavior in realistic scientific settings.
What's missing
The paper is a preprint and has not yet undergone peer review. It is also unclear whether equation recovery performance reliably predicts success on genuinely unknown equation discovery problems, which is a core assumption of the benchmark's design.
What different sources said
- arXiv cs.LGCenter
ERBench: A Benchmark and Testsuite for Equation Discovery Algorithms
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