Equation discovery with Bayesian tree-adjoining grammars

Christopher A. Lindley; Nikolaos Dervilis; Keith Worden

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arXiv · 2609.31368

Equation discovery with Bayesian tree-adjoining grammars

Christopher A. Lindley·Nikolaos Dervilis·Keith Worden

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Abstract

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.

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Christopher A. Lindley, Nikolaos Dervilis, Keith Worden. 2026-09-25. Equation discovery with Bayesian tree-adjoining grammars. https://arxiv.org/abs/2609.31368

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