发表机构
Indian Institute of Space Science and Technology（印度空间科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种神经符号回归框架，将神经网络作为符号发现的预处理器，结合LASSO与分布式超参数优化，在Nguyen基准上的实验显示其性能优于SINDy及未调参神经基线，为科学机器学习提供了可扩展的神经符号方法。
AI 中文摘要
符号回归（SR）旨在找到简洁的数学表达式来表征数据中的基本关系，其可解释性和科学理解能力优于黑箱模型。然而，遗传编程等传统方法面临可扩展性挑战且对噪声高度敏感；SINDy等稀疏回归技术则严重依赖预先确定的特征库。本研究提出一种神经符号回归（NSR）框架，将神经网络作为符号发现的函数预处理器，采用解耦流程：神经网络先在感知交互的非线性特征空间中学习目标函数的平滑、抗噪声近似，再应用LASSO提取稀疏、可解释的闭式表达式；通过将分布式超参数优化与Ray Tune及ASHA调度集成，以提升预测精度和符号保真度。在Nguyen基准套件上的实验表明，本方法在RMSE、噪声鲁棒性和分布外泛化能力上始终优于SINDy及未调参的神经基线模型；消融研究证实了特征交互、神经网络深度及调参策略的重要性。总体而言，本研究提出了一种可扩展且可理解的神经符号框架，在神经近似与科学机器学习的稀疏方程发现之间建立了坚实的联系。
英文摘要
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.
Comments11 pages, 5 tables, 5 figures, contains detailed mathematics behind the algorithm
