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In recent years, symbolic regression has been of wide interest to provide an interpretable symbolic representation of potentially large data relationships. Initially circled to genetic algorithms, symbolic regression methods now include a…

Machine Learning · Computer Science 2022-02-10 Laure Crochepierre , Lydia Boudjeloud-Assala , Vincent Barbesant

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 is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…

Machine Learning · Computer Science 2022-09-15 Fabricio Olivetti de Franca , Gabriel Kronberger

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

Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and…

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

Learning symbolic turbulence models from indirect observation data is of significant interest as it not only improves the accuracy of posterior prediction but also provides explicit model formulations with good interpretability. However, it…

Fluid Dynamics · Physics 2025-05-12 Chutian Wu , Xin-Lei Zhang , Duo Xu , Guowei He

Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…

Machine Learning · Computer Science 2025-10-10 Ryan T. Tymkow , Benjamin D. Schnapp , Mojtaba Valipour , Ali Ghodshi

Learning symbolic expressions directly from experiment data is a vital step in AI-driven scientific discovery. Nevertheless, state-of-the-art approaches are limited to learning simple expressions. Regressing expressions involving many…

Neural and Evolutionary Computing · Computer Science 2023-06-16 Nan Jiang , Yexiang Xue

In nature, the behaviors of many complex systems can be described by parsimonious math equations. Automatically distilling these equations from limited data is cast as a symbolic regression process which hitherto remains a grand challenge.…

Machine Learning · Computer Science 2023-05-25 Yilong Xu , Yang Liu , Hao Sun

We consider the problem of learning free-form symbolic expressions from raw data, such as that produced by an experiment in any scientific domain. Accurate and interpretable models of scientific phenomena are the cornerstone of scientific…

Machine Learning · Computer Science 2021-12-09 Nikos Arechiga , Francine Chen , Yan-Ying Chen , Yanxia Zhang , Rumen Iliev , Heishiro Toyoda , Kent Lyons

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 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

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

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…

Symbolic Computation · Computer Science 2026-02-13 Nan Jiang , Ziyi Wang , Yexiang Xue

A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate…

Artificial Intelligence · Computer Science 2023-09-15 Maonian Wu , Bang Chen , Shaojun Zhu , Bo Zheng , Wei Peng , Mingyi Zhang

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at…

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 propose SatelliteFormula, a novel symbolic regression framework that derives physically interpretable expressions directly from multi-spectral remote sensing imagery. Unlike traditional empirical indices or black-box learning models,…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Zhenyu Yu , Mohd. Yamani Idna Idris , Pei Wang , Yuelong Xia , Fei Ma , Rizwan Qureshi

Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing…

Machine Learning · Computer Science 2026-03-31 Giorgio Morales , John W. Sheppard