Physics-Informed Machine Learning for Uncertainty Reduction in Time Response Reconstruction of a Dynamic System

This study proposes a hybrid method for leveraging physics-based and data-driven modeling. It is used to model a dynamic system and specifically, the reconstruction of its time response. This method relies on the idea of measuring the confidence level of the data-driven model on its predictions and using the physics-based model proportional to the uncertainty of those predictions. The Gaussian process (GP) as a data-efficient machine learning approach is used for data-driven modeling and its ability to quantify the uncertainty of predictions enables incorporation of the physics-based model. This integration is controlled by an alignment model which determines the weight of predictions of the physics-based and data-driven models. In a case study, the proposed method is used for reconstruction of a time response of a nonlinear pendulum. Postprocessing of the results shows a notable reduction in uncertainty of predictions. In addition, improvement in the hybrid model’s performance measures can be observed as well.