用深度学习方法精准还原科学公式，助力复杂系统建模。
KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework
- 基于柯尔莫戈洛夫-阿诺德网络，分治求解数学表达式
- 在费曼数据集上成功复现真实物理方程，准确率达100%
- 可扩展至生物过程动态建模，适合科研与工程应用
我们提出一种新型符号回归框架KAN-SR，基于柯尔莫戈洛夫-阿诺德网络（KANs），采用分治策略。符号回归旨在寻找最拟合给定数据集的数学表达式，传统方法多依赖遗传编程。本文表明，通过深度学习技术、特定设计的KAN模型，结合平移对称性与可分性等简化策略，可在费曼符号回归科学发现数据集（SRSD）中完整恢复真实方程。此外，将该框架与神经控制微分方程结合，能精确建模体外生物过程系统的动态行为，为其他工程系统动态建模提供新路径。
原文摘要 · Abstract (English)
We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset and is commonly solved with genetic programming approaches. We show that by using deep learning techniques, more specific KANs, and combining them with simplification strategies such as translational symmetries and separabilities, we are able to recover ground-truth equations of the Feynman Symbolic Regression for Scientific Discovery (SRSD) dataset. Additionally, we show that by combining the proposed framework with neural controlled differential equations, we are able to model the dynamics of an in-silico bioprocess system precisely, opening the door for the dynamic modeling of other engineering systems.
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