Jul 2026· IEEE Transactions on Pattern Analysis and Machine Intelligence· Vol PP, pp. 1-13· 0 citations
Medicine
TL;DR
SymBOL accurately recovers governing equations and provides interpretable pathways for equation discovery when applied to real-world systems in materials science and epidemiology, and underscores the potential of SymBOL for advancing scientific discovery.
Abstract
Symbolic Regression (SR) is a core challenge in both physics and artificial intelligence, aiming to identify mathematical equations from experimental data. Recent impressive advancements in Large Language Model (LLM)-based SR methods have addressed the limitations of traditional approaches in flexibly incorporating prior knowledge to enhance accuracy, but they still face challenges such as high costs and scalability with numerous variables. To overcome these issues, we introduce SymBOL. This general-purpose symbolic learning framework uses Bayesian Optimization (BO) to guide the generation of high-quality mathematical expressions from the LLM while accommodating complex tasks with a large number of interdependent variables. Experiments on benchmark datasets demonstrate that SymBOL significantly outperforms baseline methods in both accuracy and efficiency. Notably, compared to advanced LLM-based approaches, SymBOL achieves a 24.85% improvement in average accuracy while reducing computational costs by 28.73%. This advantage extends to high-dimensional SR tasks, where SymBOL substantially lowers the average error. Furthermore, when applied to real-world systems in materials science and epidemiology, SymBOL accurately recovers governing equations and provides interpretable pathways for equation discovery. These findings underscore the potential of SymBOL for advancing scientific discovery.
Multi-Objective Tool-augmented Symbolic Regression (MOT-SR), a unified framework that integrates external analytical tools to extract structural priors and guide equation generation, while jointly optimizing for accuracy, complexity, and generalization via a multi-objective evaluation module that maintains a dynamic Pareto front is proposed.
Boxiao Wang, Runxian Wang, Kai Li et al.· arXiv.org· 0 citations
Symbolic regression (SR), the automated discovery of mathematical expressions from data, is a cornerstone of scientific inquiry. However, it is often hindered by the combinatorial explosion of the search space and a tendency to overfit. Popular methods, rooted in genetic programming, explore this space syntactically, often yielding overly complex, uninterpretable models. This paper introduces IdeaSearchFitter, a framework that employs Large Language Models (LLMs) as semantic operators within an evolutionary search. By generating candidate expressions guided by natural-language rationales, our method biases discovery towards models that are not only accurate but also conceptually coherent and interpretable. We demonstrate IdeaSearchFitter's efficacy across diverse challenges: it achieves competitive, noise-robust performance on the Feynman Symbolic Regression Database (FSReD), outperforming several strong baselines; discovers mechanistically aligned models with good accuracy-complexity trade-offs on real-world data; and derives compact, physically-motivated parametrizations for Parton Distribution Functions in a frontier high-energy physics application. IdeaSearchFitter is a specialized module within our broader iterated agent framework, IdeaSearch, which is publicly available at \href{https://www.ideasearch.cn/}{https://www.ideasearch.cn/}.
Zhuo-Yang Song, Ze-Yu Cai, Shu-Tao Zhang et al.· Communications in Theoretica...· 0 citations
This paper combines symbolic regression with LLMs for feature engineering (SymboLLM-FE) to solve the dual challenges of poor interpretability and numerous iterations by employing a statistical prior-grounded LLM refinement mechanism and single-digit LLM calls.
Zi-Jian Cheng, Zi-Yi Jia, Zhi Zhou et al.· 0 citations
This survey comprehensively analyzes contemporary symbolic regression methodologies by systematically integrating four paradigmatic approaches: deterministic methods, metaheuristic algorithms, neural-symbolic frameworks, and emerging hybrid strategies, establishing a unified taxonomic framework that bridges evolutionary computation, mathematical programming, and deep learning paradigms.
Vikas Palakonda, Samira Ghorbanpour, Sangseok Yun et al.· Archives of Computational Me...· 0 citations
Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.
Symbolic regression (SR) discovers closed-form mathematical expressions from data, offering interpretability beyond black-box models. Existing methods suffer from slow convergence in combinatorial search spaces and lack mechanisms to exploit compositional structure in the data. We introduce SMILE (Sine, Multiplication, Identity, Logarithm, Exponential), a hybrid framework that unifies continuous gradient-based optimization with discrete symbolic recovery through three stages: structural analysis of the data to identify the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network that encodes the target expression using interpretable activations, and symbolic recovery through structured pruning, coefficient optimization, and rounding. This final stage distills the learned network into a compact expression with exact symbolic constants. We evaluate SMILE on SRBench across ground-truth and black-box datasets, with ablation studies validating each component. SMILE achieves the highest symbolic solution rate at the largest noise levels, demonstrating strong robustness where competing methods degrade substantially. It consistently lies on the Pareto front of accuracy versus complexity, recovering significantly simpler expressions in a fraction of the time required by the competing methods.
Mansooreh Montazerin, Antonio Ortega, Ajitesh Srivastava· 0 citations
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