用KAN网络结合稀疏识别法，自动发现简洁的非线性动力系统方程。
SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks
- 让KAN的每个激活函数都满足稀疏识别约束，提升可解释性
- 在多个动力系统上准确恢复出真实方程，误差低于5%
- 适合需要可解释模型的科学建模场景
Kolmogorov-Arnold网络（KANs）为提升机器学习的可解释性提供了新思路，但其学习到的解未必具有稀疏性或简洁性。稀疏识别非线性动力学（SINDy）是一种从数据中学习稀疏方程的方法，但受限于预定义的项库。本文提出SINDy-KANs，通过联合训练一个KAN和一个类似SINDy的表示，在每个激活函数层面应用SINDy，既保留了深度KAN的函数组合能力，又增强了表示的可解释性。我们在多个符号回归任务（包括动力系统）上验证该方法，结果表明能准确发现各类系统的解析方程。
原文摘要 · Abstract (English)
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.
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