Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow

Xu，Rui1; Zhang，Dongxiao2; Rong，Miao1; Wang，Nanzhe3

2021-07-01

10.1016/j.jcp.2021.110318

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

Deep neural networks (DNNs) are widely used as surrogate models, and incorporating theoretical guidance into DNNs has improved generalizability. However, most such approaches define the loss function based on the strong form of conservation laws (via partial differential equations, PDEs), which is subject to diminished accuracy when the PDE has high-order derivatives or the solution has strong discontinuities. Herein, we propose a weak form Theory-guided Neural Network (TgNN-wf), which incorporates the weak form residual of the PDE into the loss function, combined with data constraint and initial and boundary condition regularizations, to overcome the aforementioned difficulties. The original loss minimization problem is reformulated into a Lagrangian duality problem, so that the weights of the terms in the loss function are optimized automatically. We use domain decomposition with locally-defined test functions, which captures local discontinuity effectively. Two numerical cases demonstrate the superiority of the proposed TgNN-wf over the strong form TgNN, including hydraulic head prediction for unsteady-state 2D single-phase flow problems and saturation profile prediction for 1D two-phase flow problems. Results show that TgNN-wf consistently achieves higher accuracy than TgNN, especially when strong discontinuity in the parameter or solution space is present. TgNN-wf also trains faster than TgNN when the number of integration subdomains is not too large (<10,000). Furthermore, TgNN-wf is more robust to noise. Consequently, the proposed TgNN-wf paves the way for which a variety of deep learning problems in small data regimes can be solved more accurately and efficiently.

Lagrangian duality Single-phase flow Theory-guided neural network Two-phase flow Weak form

SCI ; EI

英语

通讯

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000746492700016

ACADEMIC PRESS INC ELSEVIER SCIENCE

20211410182508

Boundary conditions ; Deep neural networks ; Domain decomposition methods ; Neural networks ; Two phase flow

Fluid Flow, General:631.1 ; Numerical Methods:921.6

PHYSICS

2-s2.0-85103574842

Scopus

1.Intelligent Energy Laboratory,Peng Cheng Laboratory,Guangdong,China
2.School of Environmental Science and Engineering,Southern University of Science and Technology,Guangdong,China
3.College of Engineering,Peking University,Beijing,China

Xu，Rui,Zhang，Dongxiao,Rong，Miao,et al. Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2021,436.

Xu，Rui,Zhang，Dongxiao,Rong，Miao,&Wang，Nanzhe.(2021).Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow.JOURNAL OF COMPUTATIONAL PHYSICS,436.

Xu，Rui,et al."Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow".JOURNAL OF COMPUTATIONAL PHYSICS 436(2021).