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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

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Data Analysis, Statistics and Probability · Physics 2016-08-03 Markus Quade , Markus Abel , Kamran Shafi , Robert K. Niven , Bernd R. Noack

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…

Symbolic Computation · Computer Science 2023-08-17 Julia Balla , Sihao Huang , Owen Dugan , Rumen Dangovski , Marin Soljacic

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

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…

We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…

High Energy Physics - Experiment · Physics 2025-07-04 Ho Fung Tsoi , Dylan Rankin , Cecile Caillol , Miles Cranmer , Sridhara Dasu , Javier Duarte , Philip Harris , Elliot Lipeles , Vladimir Loncar

Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…

Machine Learning · Computer Science 2026-03-31 Viktor Martinek , Roland Herzog

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

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

This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach…

Machine Learning · Computer Science 2024-11-07 MZ Naser , Ahmed Z Naser

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained…

Machine Learning · Computer Science 2023-10-31 Parshin Shojaee , Kazem Meidani , Amir Barati Farimani , Chandan K. Reddy

Mathematical expressions play a central role in scientific discovery. Symbolic regression aims to automatically discover such expressions from given numerical data. Recently, Neural symbolic regression (NSR) methods that involve…

Machine Learning · Computer Science 2026-02-03 Shun Sato , Issei Sato

Imitation learning is a popular method for teaching robots new behaviors. However, most existing methods focus on teaching short, isolated skills rather than long, multi-step tasks. To bridge this gap, imitation learning algorithms must not…

Artificial Intelligence · Computer Science 2025-11-04 Leon Keller , Daniel Tanneberg , Jan Peters

Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…

Machine Learning · Computer Science 2022-06-29 Stéphane d'Ascoli , Pierre-Alexandre Kamienny , Guillaume Lample , François Charton

Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities…

Geophysics · Physics 2023-11-22 Dion Häfner , Johannes Gemmrich , Markus Jochum

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

Artificial Intelligence · Computer Science 2024-11-12 Jiao Hu , Jiaxu Cui , Bo Yang

A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…

Combinatorics · Mathematics 2021-01-22 E. Di Nardo , D. Senato

Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…

Machine Learning · Computer Science 2025-02-12 Yuan Tian , Wenqi Zhou , Michele Viscione , Hao Dong , David Kammer , Olga Fink

Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…

Machine Learning · Computer Science 2025-02-14 Yuan Tian , Wenqi Zhou , Michele Viscione , Hao Dong , David Kammer , Olga Fink

Symbolic regression, the task of extracting mathematical expressions from the observed data $\{ \vx_i, y_i \}$, plays a crucial role in scientific discovery. Despite the promising performance of existing methods, most of them conduct…

Machine Learning · Computer Science 2023-02-22 Pengwei Jin , Di Huang , Rui Zhang , Xing Hu , Ziyuan Nan , Zidong Du , Qi Guo , Yunji Chen