发表机构
University of Sheffield（谢菲尔德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出贝叶斯树邻接文法框架，通过可逆跳跃MCMC推断模型结构与参数，实现动力系统方程发现中的不确定性量化，并在多项基准上验证其优于物理驱动基线。
AI 中文摘要
树邻接文法（TAGs）最近被引入非线性系统辨识（NLSI），作为一种将整个模型类编码为有限语法规则集的手段，候选模型以树的形式从这些规则中组装而成。现有的基于TAG的辨识器依赖进化优化，并返回模型结构的点估计。本文转而提出在贝叶斯框架下的TAG方法。在树结构及其参数上定义了一个生成式先验，并使用带有结构保持树移动的可逆跳跃MCMC采样器来推断模型结构、参数和预测的联合后验。考虑了两种训练目标：一种是带有共轭参数提议的单步超前目标，另一种是基于模拟的似然自由推断目标。该方法在模拟多项式NARX系统、Silverbox基准以及来自Christchurch Bay Tower的波浪载荷数据上进行了验证，其中将Morison方程作为固定初始树嵌入，产生了一个优于物理驱动基线的灰盒模型。结果表明，贝叶斯TAG非常适用于量化动力系统方程发现中的不确定性，以及拟合物理信息模型。
英文摘要
Tree-Adjoining Grammars (TAGs) have recently been introduced to Nonlinear System Identification (NLSI) as a means of encoding an entire model class as a finite set of grammatical rules, from which candidate models are assembled as trees. Existing TAG-based identifiers rely on evolutionary optimisation and return point estimates of the model structure. This paper instead proposes the TAG framework within a Bayesian setting. A generative prior is defined over tree structures and their parameters, and a Reversible-Jump MCMC sampler with structure-preserving tree moves is used to infer the joint posterior over model structure, parameters and predictions. Two training objectives are considered; that is, a one-step-ahead objective with conjugate parameter proposals, and a simulation-based objective handled by likelihood-free inference. The approach is validated on a simulated polynomial NARX system, the Silverbox benchmark, and wave-loading data from the Christchurch Bay Tower, where embedding Morison's equation as a fixed initial tree yields a grey-box model that outperforms the physics-driven baseline. The results demonstrate that Bayesian TAGs are well suited to quantifying uncertainty in equation discovery for dynamical systems and to fitting physics-informed models.
