标题： 贝叶斯广义非线性模型为无基础的SINDy提供了模型不确定性 显示英文标题

标题： Bayesian Generalized Nonlinear Models Offer Basis Free SINDy With Model Uncertainty

摘要： 稀疏非线性动力学识别（SINDy）已成为一种标准方法，用于从观测数据中通过统计建模推断动力系统的控制方程。 然而，传统的SINDy方法依赖于预定义的候选函数库来模拟非线性，这限制了灵活性并排除了稳健的不确定性量化。 本文提出贝叶斯广义非线性模型（BGNLMs）作为一种更有原则性的替代方法，以实现更灵活的统计建模。 BGNLMs 使用尖峰-滑板先验结合二进制包含指示器，无需预定义基函数即可自动发现相关的非线性。 此外，BGNLMs 量化选定基函数和最终模型预测中的不确定性，从而实现对模型空间的稳健探索。 在本文中，BGNLM 框架被应用于几个三维（3D）SINDy 问题。 显示英文摘要

摘要： Sparse Identification of Nonlinear Dynamics (SINDy) has become a standard methodology for inferring governing equations of dynamical systems from observed data using statistical modeling. However, classical SINDy approaches rely on predefined libraries of candidate functions to model nonlinearities, which limits flexibility and excludes robust uncertainty quantification. This paper proposes Bayesian Generalized Nonlinear Models (BGNLMs) as a principled alternative for more flexible statistical modeling. BGNLMs employ spike-and-slab priors combined with binary inclusion indicators to automatically discover relevant nonlinearities without predefined basis functions. Moreover, BGNLMs quantify uncertainty in selected bases and final model predictions, enabling robust exploration of the model space. In this paper, the BGNLM framework is applied to several three-dimensional (3D) SINDy problems.