Machine learning subsurface flow equations from data
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Governing equations of physical problems are traditionally derived from conservation laws or physical principles. However, some complex problems still exist for which these first-principle derivations cannot be implemented. As data acquisition and storage ability have increased, data-driven methods have attracted great attention. In recent years, several works have addressed how to learn dynamical systems and partial differential equations using data-driven methods. Along this line, in this work, we investigate how to discover subsurface flow equations from data via a machine learning technique, the least absolute shrinkage and selection operator (LASSO). The learning of single-phase groundwater flow equation and contaminant transport equation are demonstrated. Considering that the parameters of subsurface formation are usually heterogeneous, we propose a procedure for learning partial differential equations with heterogeneous model parameters for the first time. Derivative calculation from discrete data is required for implementing equation learning, and we discuss how to calculate derivatives from noisy data. For a series of cases, the proposed data-driven method demonstrates satisfactory results for learning subsurface flow equations.
KeywordsMachine learning Data-driven discovery Governing equations Noisy data LASSO
This work is partially funded by the National Natural Science Foundation of China (Grant No. U1663208 and 51520105005) and the National Science and Technology Major Project of China (Grant No. 2017ZX05009-005 and 2016ZX05037-003). The link for the open-source Matlab code is provided in Hesterberg et al. . The other computer codes and data used are available upon request from the corresponding author.
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Conflict of interests
The authors declare that they have no conflict of interest.
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