Solution of diffusivity equations with local sources/sinks and surrogate modeling using weak form Theory-guided Neural Network

Xu，Rui1; Wang，Nanzhe2; Zhang，Dongxiao3

2021-07-01

10.1016/j.advwatres.2021.103941

ADVANCES IN WATER RESOURCES   影响因子和分区

0309-1708

1872-9657

Neural-network-based surrogate models are widely used to improve computational efficiency. Incorporating theoretical guidance into data-driven neural networks has improved their generalizability and accuracy. However, neural networks with strong form (partial differential equations) theoretical guidance have limited performance when strong discontinuity exists in the solution spaces, such as pressure discontinuity at sources/sinks in subsurface flow problems. In this study, we take advantage of weak form formulation and domain decomposition to deal with such difficulties. We propose two strategies based on our previously developed weak form Theory-guided Neural Network (TgNN-wf) to solve diffusivity equations with point sinks of either Dirichlet or Neumann type. Surrogate models are trained for well placement optimization and uncertainty analysis. Good agreement with numerical results is observed at lower computational costs, whereas strong form TgNN fails to provide satisfactory results, indicating the superiority of weak form formulation when solving discontinuous problems.

Diffusivity equation Surrogate modeling Theory-guided Neural Network Uncertainty analysis Weak form Well placement optimization

SCI ; EI

英语

通讯

Water Resources

Water Resources

WOS:000670306000003

ELSEVIER SCI LTD

20212110402904

Computation theory ; Computational efficiency ; Domain decomposition methods ; Uncertainty analysis

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Numerical Methods:921.6 ; Probability Theory:922.1

ENGINEERING

2-s2.0-85106220310

Scopus

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

Xu，Rui,Wang，Nanzhe,Zhang，Dongxiao. Solution of diffusivity equations with local sources/sinks and surrogate modeling using weak form Theory-guided Neural Network[J]. ADVANCES IN WATER RESOURCES,2021,153.

Xu，Rui,Wang，Nanzhe,&Zhang，Dongxiao.(2021).Solution of diffusivity equations with local sources/sinks and surrogate modeling using weak form Theory-guided Neural Network.ADVANCES IN WATER RESOURCES,153.

Xu，Rui,et al."Solution of diffusivity equations with local sources/sinks and surrogate modeling using weak form Theory-guided Neural Network".ADVANCES IN WATER RESOURCES 153(2021).