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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

Symbolic regression (SR) is the task of learning a model of data in the form of a mathematical expression. By their nature, SR models have the potential to be accurate and human-interpretable at the same time. Unfortunately, finding such…

Neural and Evolutionary Computing · Computer Science 2022-07-12 Marco Virgolin , Solon P. Pissis

Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive…

Machine Learning · Computer Science 2024-04-30 Qing Li , Yixin Zhu , Yitao Liang , Ying Nian Wu , Song-Chun Zhu , Siyuan Huang

Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem…

Neural and Evolutionary Computing · Computer Science 2021-11-19 T. Nathan Mundhenk , Mikel Landajuela , Ruben Glatt , Claudio P. Santiago , Daniel M. Faissol , Brenden K. Petersen

Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression…

Machine Learning · Computer Science 2025-03-13 Sikai Huang , Yixin Berry Wen , Tara Adusumilli , Kusum Choudhary , Haizhao Yang

Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…

Machine Learning · Computer Science 2021-02-16 Li Li , Minjie Fan , Rishabh Singh , Patrick Riley

This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is…

Machine Learning · Computer Science 2022-03-22 Daniel Rivero , Enrique Fernandez-Blanco

Symbolic regression is the task of identifying a mathematical expression that best fits a provided dataset of input and output values. Due to the richness of the space of mathematical expressions, symbolic regression is generally a…

Machine Learning · Computer Science 2021-06-29 Mojtaba Valipour , Bowen You , Maysum Panju , Ali Ghodsi

Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is…

Computer Vision and Pattern Recognition · Computer Science 2022-06-16 Jiachen Li , Ye Yuan , Hong-Bin Shen

Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…

Machine Learning · Computer Science 2026-01-13 Mikhail Lazarev , Andrey Ustyuzhanin

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods…

Machine Learning · Computer Science 2024-12-11 Arya Grayeli , Atharva Sehgal , Omar Costilla-Reyes , Miles Cranmer , Swarat Chaudhuri

Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to…

Machine Learning · Computer Science 2022-09-07 Daniel M. DiPietro , Bo Zhu

Symbolic regression (SR) aims to discover the underlying mathematical expressions that explain observed data. This holds promise for both gaining scientific insight and for producing inherently interpretable and generalizable models for…

Machine Learning · Computer Science 2026-02-05 David Otte , Jörg K. H. Franke , Arbër Zela , Fábio Ferreira , Frank Hutter

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

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…

Machine Learning · Computer Science 2024-05-14 Tony Tohme , Mohammad Javad Khojasteh , Mohsen Sadr , Florian Meyer , Kamal Youcef-Toumi

Neuro-encoded expression programming(NEEP) that aims to offer a novel continuous representation of combinatorial encoding for genetic programming methods is proposed in this paper. Genetic programming with linear representation uses…

Neural and Evolutionary Computing · Computer Science 2021-04-12 Aftab Anjum , Fengyang Sun , Lin Wang , Jeff Orchard

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep…

Machine Learning · Computer Science 2023-12-04 Sida Li , Ioana Marinescu , Sebastian Musslick

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

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…

Methodology · Statistics 2025-09-25 Somjit Roy , Pritam Dey , Debdeep Pati , Bani K. Mallick

Symbolic Regression (SR) searches for mathematical expressions which best describe numerical datasets. This allows to circumvent interpretation issues inherent to artificial neural networks, but SR algorithms are often computationally…

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