Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 393, Issue -, Pages 337-350Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.05.008
Keywords
PDE discovery; Data driven method; Data assimilation method; Physical processes; Solute transport
Funding
- National Natural Science Foundation of China [U1663208, 51520105005]
- National Science and Technology Major Project of China [2017ZX05009-005, 2016ZX05037-003]
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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 datadriven 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. (C) 2019 Elsevier Inc. All rights reserved.
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