SINDy-KANs：通过Kolmogorov-Arnold网络进行非线性动力学的稀疏识别
SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks
AI总结：
本文提出SINDy-KANs方法，结合KAN和SINDy，通过每个激活函数层面的应用提升KAN的可解释性，同时保持深度KAN的功能组合能力，用于符号回归任务中的方程发现。
摘要：
Kolmogorov-Arnold网络（KANs）作为一种增强机器学习可解释性的潜在方法，但其学习到的解决方案未必具有可解释性，即稀疏或简洁。稀疏非线性动力学识别（SINDy）是一种互补方法，允许从数据中学习稀疏方程用于动力系统；然而，学习的方程受库的限制。在本文中，我们提出了SINDy-KANs，同时训练KAN和SINDy-like表示，以提高KAN表示的可解释性，通过在每个激活函数层面应用SINDy，同时保持通过深度KAN可能的功能组合。我们将其应用于多个符号回归任务，包括动力系统，以展示在各种系统中准确的方程发现。
英文摘要：
Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complementary approach that allows for learning sparse equations for dynamical systems from data; however, learned equations are limited by the library. In this work, we present SINDy-KANs, which simultaneously train a KAN and a SINDy-like representation to increase interpretability of KAN representations with SINDy applied at the level of each activation function, while maintaining the function compositions possible through deep KANs. We apply our method to a number of symbolic regression tasks, including dynamical systems, to show accurate equation discovery across a range of systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
