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Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Dynamical Systems · Mathematics 2026-05-07 Nibodh Boddupalli , Timothy Matchen , Jeff Moehlis

Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this…

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…

Machine Learning · Statistics 2025-07-29 Roger Guimera , Marta Sales-Pardo

Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the…

Machine Learning · Computer Science 2022-04-25 Pierre-Alexandre Kamienny , Stéphane d'Ascoli , Guillaume Lample , François Charton

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

Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…

Instrumentation and Methods for Astrophysics · Physics 2025-07-18 Harry Desmond

This tutorial paper provides a general overview of symbolic regression (SR) with specific focus on standards of interpretability. We posit that interpretable modeling, although its definition is still disputed in the literature, is a…

Machine Learning · Computer Science 2023-06-02 Jennifer J. Schnur , Nitesh V. Chawla

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…

Machine Learning · Computer Science 2020-04-28 J. Kubalík , E. Derner , R. Babuška

The mathematical formula is the human language to describe nature and is the essence of scientific research. Finding mathematical formulas from observational data is a major demand of scientific research and a major challenge of artificial…

Machine Learning · Computer Science 2024-04-10 Yanjie Li , Weijun Li , Lina Yu , Min Wu , Jingyi Liu , Wenqiang Li , Meilan Hao , Shu Wei , Yusong Deng

Symbolic Regression tries to find a mathematical expression that describes the relationship of a set of explanatory variables to a measured variable. The main objective is to find a model that minimizes the error and, optionally, that also…

Artificial Intelligence · Computer Science 2018-02-27 Fabricio Olivetti de Franca

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

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

Machine Learning · Computer Science 2025-06-25 Paul Kahlmeyer , Joachim Giesen , Michael Habeck , Henrik Voigt

The typical methods for symbolic regression produce rather abrupt changes in solution candidates. In this work, we have tried to transform symbolic regression from an optimization problem, with a landscape that is so rugged that typical…

Machine Learning · Computer Science 2021-08-10 Erik Pitzer , Gabriel Kronberger

Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…

Machine Learning · Computer Science 2026-02-03 Xinxin Li , Juan Zhang , Da Li , Xingyu Liu , Jin Xu , Junping Yin

Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…

Machine Learning · Computer Science 2024-06-11 Tim Schneider , Amin Totounferoush , Wolfgang Nowak , Steffen Staab

We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR…

High Energy Physics - Phenomenology · Physics 2024-12-12 Manuel Morales-Alvarado , Daniel Conde , Josh Bendavid , Veronica Sanz , Maria Ubiali

Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…

Neural and Evolutionary Computing · Computer Science 2024-02-12 Kirill Antonov , Roman Kalkreuth , Kaifeng Yang , Thomas Bäck , Niki van Stein , Anna V Kononova

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

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

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