Probabilistic modeling by integrating data and physical model for application to space-time data

Abstract

It is essential to obtain a precise model for simulation and control. Grey-box modeling is one of the modeling methods that aims to effectively acquire real-world behaviors by integrating physical models and data. Besides, it is also significant to evaluate the uncertainty of the model. In this research, we extended the grey-box modeling method that learns differential equations and proposed the probabilistic grey-box modeling method to predict distributions of outputs. By applying this method to the space-time simulation data with process noise, we showed its ability to estimate the mean and variance of outputs. In addition, according to the result of the comparison with the data-driven model, it was suggested that integrating the physical model was effective when an adequate amount of data was unavailable.