Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data

Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data Junsheng Zeng, Hao Xu, Yuntian Chen, and Dongxiao Zhang 1 Frontier Research Center, Peng Cheng Laboratory, Shenzhen 518000, P. R. China 2 College of Engineering, Peking University, Beijing 100871, P. R. China 3 School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, P. R. China

[1]  A. Hogg,et al.  Draining viscous gravity currents in a vertical fracture , 2002, Journal of Fluid Mechanics.

[2]  Anna V. Kaluzhnaya,et al.  Data-driven PDE discovery with evolutionary approach , 2019, ICCS.

[3]  Paris Perdikaris,et al.  Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..

[4]  H. A. Kendall,et al.  Gravity Segregation of Miscible Fluids in Linear Models , 1962 .

[5]  L. Chiapponi,et al.  Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium , 2017, Journal of Fluid Mechanics.

[6]  Hao Xu,et al.  DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm , 2020, J. Comput. Phys..

[7]  J. Anderson,et al.  Computational fluid dynamics : the basics with applications , 1995 .

[8]  Steven L. Brunton,et al.  Methods for data-driven multiscale model discovery for materials , 2019, Journal of Physics: Materials.

[9]  OlssonElin,et al.  A conservative level set method for two phase flow , 2005 .

[10]  Chi-Wang Shu,et al.  Total variation diminishing Runge-Kutta schemes , 1998, Math. Comput..

[11]  Kaj Nyström,et al.  Data-driven discovery of PDEs in complex datasets , 2018, J. Comput. Phys..

[12]  Guang Lin,et al.  Robust data-driven discovery of governing physical laws with error bars , 2018, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  Haibin Chang,et al.  Machine learning subsurface flow equations from data , 2019, Computational Geosciences.

[14]  A. Woods.  LIQUID AND VAPOR FLOW IN SUPERHEATED ROCK , 1999 .

[15]  E Kaiser,et al.  Sparse identification of nonlinear dynamics for model predictive control in the low-data limit , 2017, Proceedings of the Royal Society A.

[16]  I. Christov,et al.  Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents , 2014, Journal of Fluid Mechanics.

[17]  A. Werner.  On the classification of seawater intrusion , 2017 .

[18]  Dongxiao Zhang,et al.  Robust discovery of partial differential equations in complex situations , 2021, Physical Review Research.

[19]  Alessandro Lenci,et al.  Dispersion induced by non-Newtonian gravity flow in a layered fracture or formation , 2020, Journal of Fluid Mechanics.

[20]  Hao Xu,et al.  Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data , 2020, J. Comput. Phys..

[21]  Steven L. Brunton,et al.  Data-driven discovery of partial differential equations , 2016, Science Advances.

[22]  Hao Xu,et al.  DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data , 2019, Communications in Computational Physics.

[23]  Joachim Denzler,et al.  Deep learning and process understanding for data-driven Earth system science , 2019, Nature.

[24]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[25]  Stephen H. Davis,et al.  Spreading and imbibition of viscous liquid on a porous base , 1998 .

[26]  D. Chan,et al.  Numerical simulation of proppant transport in hydraulic fractures , 2018 .

[27]  Steven L Brunton,et al.  Sparse identification of nonlinear dynamics for rapid model recovery. , 2018, Chaos.

[28]  V. Di Federico,et al.  A dipole solution for power-law gravity currents in porous formations , 2015, Journal of Fluid Mechanics.

[29]  Christopher Kadow,et al.  Artificial intelligence reconstructs missing climate information , 2020, Nature Geoscience.

[30]  A. Woods,et al.  On the slow draining of a gravity current moving through a layered permeable medium , 2001, Journal of Fluid Mechanics.

[31]  Steven L. Brunton,et al.  Data-Driven Identification of Parametric Partial Differential Equations , 2018, SIAM J. Appl. Dyn. Syst..

[32]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[33]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[34]  D. A. Barry,et al.  Seawater intrusion processes, investigation and management: Recent advances and future challenges , 2013 .

[35]  Paris Perdikaris,et al.  Machine learning of linear differential equations using Gaussian processes , 2017, J. Comput. Phys..

[36]  A. Woods,et al.  The dynamics of two-layer gravity-driven flows in permeable rock , 2000, Journal of Fluid Mechanics.

[37]  P. Baldi,et al.  Searching for exotic particles in high-energy physics with deep learning , 2014, Nature Communications.

[38]  Ismael Herrera,et al.  Enhanced Oil Recovery , 2012 .

[39]  Ribana Roscher,et al.  Explainable Machine Learning for Scientific Insights and Discoveries , 2019, IEEE Access.

[40]  Y. Notay.  An aggregation-based algebraic multigrid method , 2010 .