A sparse Bayesian approach to model structure selection and parameter estimation of dynamical systems using spike-and-slab priors

In this study, a data-driven equation discovery approach is followed for simultaneous model structure selection and parameter estimation based on sparse linear regression. Adopting a Bayesian framework, a new equation discovery algorithm is proposed using spike-and-slab prior which results in models that are more parsimonious and interpretable. The proposed algorithm is applied to four systems of engineering interest, which include a baseline linear system, a cubic stiffness (Duffing oscillator), an additive quadratic viscous damping and a Coulomb damping. It is shown that the proposed algorithm is effective in identifying the presence and type of nonlinearity in the system. Additionally, comparisons with the Relevance Vector Machine - a previously proposed algorithm for Bayesian equation discovery that uses a Students't prior - indicate that the spike-and-slab priors often achieve stronger model selection consistency and derive models that have superior predictive accuracy.