On robust equation discovery: a sparse Bayesian and Gaussian process approach

Parameter estimation plays an important role in describing the characteristics of dynamic systems. In many applications however, the chosen model may not always be able to properly describe all the physics of the real system, leading to biased parameter estimation results. This paper proposes a novel parameter estimation approach through an equation discovery procedure, which allows erroneous forms in the model to be removed and model discrepancy to be properly captured simultaneously. This is achieved by introducing sparsity into the model through sparse Bayesian learning and using a non-parametric Gaussian process model to account for model discrepancy. These two methods are utilized via a Bayesian framework, allowing the parameters to be estimated in a probabilistic manner. Synthetic and experimental data are used to validate the proposed method. The results show that this new method is able to provide better estimates of the model parameters with less bias involved, thereby better identifying the physics and reducing epistemic uncertainty.