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Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless,…

Symbolic regression is a machine learning method with the goal to produce interpretable results. Unlike other machine learning methods such as, e.g. random forests or neural networks, which are opaque, symbolic regression aims to model and…

Machine Learning · Computer Science 2024-06-07 Yousef A. Radwan , Gabriel Kronberger , Stephan Winkler

Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful…

Neural and Evolutionary Computing · Computer Science 2026-05-18 Koki Ikeda , Masahiro Nomura , Ryoki Hamano

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…

Machine Learning · Computer Science 2024-06-04 Wenqiang Li , Weijun Li , Lina Yu , Min Wu , Linjun Sun , Jingyi Liu , Yanjie Li , Shu Wei , Yusong Deng , Meilan Hao

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…

Machine Learning · Computer Science 2025-09-17 Xiaoxu Han , Chengzhen Ning , Jinghui Zhong , Fubiao Yang , Yu Wang , Xin Mu

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Machine Learning · Computer Science 2026-03-25 Fateme Memar , Tao Zhe , Dongjie Wang

Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…

Machine Learning · Computer Science 2025-02-11 Ho Fung Tsoi , Vladimir Loncar , Sridhara Dasu , Philip Harris

Symbolic Regression (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently…

Machine Learning · Computer Science 2026-05-19 Cas Oude Hoekstra , Floris den Hengst

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

Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…

Machine Learning · Computer Science 2021-10-27 Ismail Alaoui Abdellaoui , Siamak Mehrkanoon

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

Symbolic Computation · Computer Science 2025-05-29 Weiting Liu , Jiaxu Cui , Jiao Hu , En Wang , Bo Yang

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…

Machine Learning · Computer Science 2026-04-10 Deaglan J. Bartlett , Harry Desmond , Pedro G. Ferreira , Gabriel Kronberger

Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved…

Machine Learning · Computer Science 2022-03-10 Samuel Kim , Peter Y. Lu , Srijon Mukherjee , Michael Gilbert , Li Jing , Vladimir Čeperić , Marin Soljačić

Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR…

Machine Learning · Computer Science 2024-08-13 Jorge Medina , Andrew D. White

Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic…

Instrumentation and Methods for Astrophysics · Physics 2023-12-27 Wassim Tenachi , Rodrigo Ibata , Foivos I. Diakogiannis

Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes,…

Machine Learning · Computer Science 2023-01-10 Tony Tohme , Dehong Liu , Kamal Youcef-Toumi

We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…

Machine Learning · Computer Science 2026-03-30 Zachary Bastiani , Robert M. Kirby , Jacob Hochhalter , Shandian Zhe

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…

Machine Learning · Computer Science 2024-09-20 Yanjie Li , Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Meilan Hao , Su Wei , Yusong Deng

Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is better reflected by the resulting models. The expected behavior is…

Machine Learning · Computer Science 2023-03-10 Christian Haider

Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains…

Machine Learning · Computer Science 2024-06-27 Giorgio Morales , John W. Sheppard