Uncertainty Quantification in Parameter Estimation Using Physics-Integrated Machine Learning

This paper proposes a hybrid physics-machine learning method for probabilistic parameter estimation of a nonlinear dynamic system. The ability of this method to quantify the uncertainty of estimations is utilized at different levels of the hybrid method. In this method, a set of physics-based features are introduced to amplify the information content of initial observations. With this objective, the perturbation method is applied to obtain the asymptotic solution and frequency response of the nonlinear system in physics-based modeling. Extracted mathematical relationships provide for the identification of root causes of changes in frequency response. Subsequently, topological changes are quantified to be used as the inputs of the machine learning model. A Gaussian process regression (GPR) model is developed as a probabilistic estimator which uses the above physics-based features. The method is demonstrated using the case study of a linearly coupled Duffing oscillator system. The effectiveness and robustness of the hybrid method are demonstrated by estimating the coupling coefficient under strong nonlinear and uncertain parameter situations.