GSR: A Generalized Symbolic Regression Approach

Abstract

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, SR attempts to gain insight into the underlying relationships between the independent variables and the target variable of a given dataset by assembling analytical functions. In this paper, we present GSR, a Generalized Symbolic Regression approach, by modifying the conventional SR optimization problem formulation, while keeping the main SR objective intact. In GSR, we infer mathematical relationships between the independent variables and some transformation of the target variable. We constrain our search space to a weighted sum of basis functions, and propose a genetic programming approach with a matrix-based encoding scheme. We show that our GSR method outperforms several state-of-the-art methods on the well-known SR benchmark problem sets. Finally, we highlight the strengths of GSR by introducing SymSet, a new SR benchmark set which is more challenging relative to the existing benchmarks.

Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws

“…As we have shown in Section 4.3, it is straightforward to improve our method by combining it with the powerful problem simplification schemes devised in (Udrescu & Tegmark 2020;Luo et al 2017;Tohme et al 2022;Cranmer et al 2020). The results of the separability procedures implemented in the ) algorithm are conveniently recorded in separate datafiles, which makes it completely straightforward to use their approach as a pre-processing step for Φ-SO.…”

“…This type of approach includes the well known Eureqa software (Schmidt & Lipson 2009) (see Graham et al 2013 for a benchmark of Eureqa's capabilities on astrophysical test cases), as well as more recent works (Cranmer 2020;Virgolin & Bosman 2022;Stephens 2015;Kommenda et al 2020;Keren et al 2023). In addition, SR has been implemented using various methods ranging from brute force to (un-)guided Monte-Carlo, all the way to probabilistic searches (Mc-Conaghy 2011;Kammerer et al 2020;Bartlett et al 2022;Brence et al 2021;Jin et al 2019), as well as through problem simplification algorithms (Luo et al 2017;Tohme et al 2022).…”

Can Artificial Intelligence Accelerate Fluid Mechanics Research?

“…On the other hand, symbolic regression (SR) is a class of ML algorithms in which mathematical equations bound exclusively to data are derived. In contrast to usual regression procedures, SR searches within a wide mathematical operator set and constants to connect input features to produce meaningful outputs [27] based on evolutionary algorithms. This process of extracting results that can be interpreted and exploited simultaneously has led to the development of numerous genetic programming-based tools that implement SR for disciplines from materials science to construction engineering to medical science [28].…”

Speeding up Genetic Programming Based Symbolic Regression Using GPUs

“…Exploring and learning relationships from data is the central challenge of the sciences. Among various methods [33,34] for achieving this goal, symbolic regression [3] which can represents such relationships as a concise and interpretable function is the most popular [32]. It has a wider range of applications in curve fitting [14], data modeling [17], and material science [35].…”