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PySR is an open-source library for practical symbolic regression, a type of machine learning which aims to discover human-interpretable symbolic models. PySR was developed to democratize and popularize symbolic regression for the sciences,…

Instrumentation and Methods for Astrophysics · Physics 2023-05-08 Miles Cranmer

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…

Machine Learning · Computer Science 2024-07-11 Xieting Chu , Hongjue Zhao , Enze Xu , Hairong Qi , Minghan Chen , Huajie Shao

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Methodology · Statistics 2020-01-17 Ying Jin , Weilin Fu , Jian Kang , Jiadong Guo , Jian Guo

This paper presents QDSR, an advanced symbolic Regression (SR) system that integrates genetic programming (GP), a quality-diversity (QD) algorithm, and a dimensional analysis (DA) engine. Our method focuses on exact symbolic recovery of…

Neural and Evolutionary Computing · Computer Science 2025-03-26 J. -P. Bruneton

The high-energy physics community is investigating the potential of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to enhance physics sensitivity while still meeting data processing time constraints. In…

Symbolic Regression (SR) is a regression method that aims to discover mathematical expressions that describe the relationship between variables, and it is often implemented through Genetic Programming, a metaphor for the process of…

Neural and Evolutionary Computing · Computer Science 2025-12-02 Guilherme Seidyo Imai Aldeia

Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the…

Machine Learning · Computer Science 2025-08-21 Viktor Martinek

The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…

Machine Learning · Computer Science 2026-01-21 Beatriz R. Brum , Luiza Lober , Isolde Previdelli , Francisco A. Rodrigues

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and…

Automating scientific discovery has been a grand goal of Artificial Intelligence (AI) and will bring tremendous societal impact. Learning symbolic expressions from experimental data is a vital step in AI-driven scientific discovery. Despite…

Artificial Intelligence · Computer Science 2023-12-20 Nan Jiang , Md Nasim , Yexiang Xue

Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert…

Machine Learning · Computer Science 2024-10-16 Haiquan Qiu , Shuzhi Liu , Quanming Yao

Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…

Machine Learning · Computer Science 2026-02-17 Jing Xiao , Xinhai Chen , Jiaming Peng , Qinglin Wang , Menghan Jia , Zhiquan Lai , Guangping Yu , Dongsheng Li , Tiejun Li , Jie Liu

This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on…

Machine Learning · Computer Science 2025-01-06 Yoshitomo Matsubara , Naoya Chiba , Ryo Igarashi , Yoshitaka Ushiku

Symbolic regression (SR) is a powerful technique for discovering symbolic expressions that characterize nonlinear relationships in data, gaining increasing attention for its interpretability, compactness, and robustness. However, existing…

Machine Learning · Statistics 2025-06-09 Shengbin Ye , Meng Li

Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional…

Machine Learning · Computer Science 2025-10-09 Yunpeng Gong , Sihan Lan , Can Yang , Kunpeng Xu , Min Jiang

Deep neural networks are susceptible to adversarial attacks due to the accumulation of perturbations in the feature level, and numerous works have boosted model robustness by deactivating the non-robust feature activations that cause model…

Computer Vision and Pattern Recognition · Computer Science 2023-03-27 Woo Jae Kim , Yoonki Cho , Junsik Jung , Sung-Eui Yoon

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…

Cosmology and Nongalactic Astrophysics · Physics 2024-08-05 Deaglan J. Bartlett , Harry Desmond , Pedro G. Ferreira

Significant pattern mining is a fundamental task in mining transactional data, requiring to identify patterns significantly associated with the value of a given feature, the target. In several applications, such as biomedicine, basket…

Machine Learning · Computer Science 2024-06-18 Leonardo Pellegrina , Fabio Vandin

Symbolic regression (SR) seeks to recover closed-form mathematical expressions that describe observed data. While existing methods have advanced the discovery of either explicit mappings (i.e., $y = f(\mathbf{x})$) or discovering implicit…

Machine Learning · Computer Science 2025-08-20 Michael Scherk , Boyuan Chen

Vertical Symbolic Regression (VSR) recently has been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by…

Machine Learning · Computer Science 2024-02-02 Nan Jiang , Md Nasim , Yexiang Xue
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