Equation discovery for nonlinear dynamical systems: A Bayesian viewpoint

This paper presents a new Bayesian approach to equation discovery – combined structure detection and parameter estimation for system identification (SI) in nonlinear structural dynamics. The is accomplished via sparsity-inducing prior within Relevance Vector Machine (RVM) framework; the ensures that terms making no contribution model are driven zero coefficient values. Motivated by idea of compressive sensing (CS) recent results from machine learning community on sparse linear regression, adopts use an over-complete dictionary represent large number candidate describing system. Unlike other learners, like Lasso its derivatives, which potentially sensitive hyperparameter selection, proposed method exploits principled means fixing priors hyperpriors available hierarchical approach. successfully demonstrated validated simulated case studies common Single-Degree-of-Freedom (SDOF) dynamic systems, two challenging experimental data sets.