Identification of physical processes via combined data-driven and data-assimilation methods

• Published in: Journal of computational physics 2019-09, Vol.393, p.337-350
• Main Authors: Chang, Haibin, Zhang, Dongxiao
• Format: Article
• Language: English
• Subjects: Computational physics; Contaminants; Data acquisition; Data assimilation method; Data driven method; Datasets; Dependence; Economic models; Empirical equations; Identification methods; Parameter estimation; Parameter identification; Parameter uncertainty; Partial differential equations; PDE discovery; Physical processes; Process parameters; Solute transport; Training
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.05.008

•An innovative framework for PDE discovery is developed by integrating data-driven and data-assimilation methods.•Physical processes and empirical models can be concurrently identified.•The developed method is applicable to complex physical problems with nonlinear models.•Discovery of the PDE of reactive solute transport in subsurface formation is investigated. With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model parameters in the equations are either assumed to be known or have a linear dependency. Therefore, most of the realistic physical processes cannot be identified with the current data-driven PDE discovery approaches. In this study, an innovative framework is developed that combines data-driven and data-assimilation methods for simultaneously identifying physical processes and inferring model parameters. Spatiotemporal measurement data are first divided into a training data set and a testing data set. Using the training data set, a data-driven method is developed to learn the governing equation of the considered physical problem by identifying the occurred (or dominated) processes and selecting the proper empirical model. Through introducing a prediction error of the learned governing equation for the testing data set, a data-assimilation method is devised to estimate the uncertain model parameters of the selected empirical model. For the contaminant solute transport problem investigated, the results demonstrate that the proposed method can adequately identify the considered physical processes via concurrently discovering the corresponding governing equations and inferring uncertain parameters of nonlinear models, even in the presence of measurement errors. This work helps to broaden the applicable area of the research of data driven discovery of governing equations of physical problems.