A fully-implicit parallel framework for complex reservoir simulation with mimetic finite difference discretization and operator-based linearization

2021 ◽  
Author(s):  
Longlong Li ◽  
Ahmad Abushaikha
Keyword(s):  
Finite Difference ◽  
Reservoir Simulation ◽  
Fully Implicit ◽  
Finite Difference Discretization ◽  
Difference Discretization

LEARNING IN RECURRENT FINITE DIFFERENCE NETWORKS

1995 ◽  
Vol 06 (03) ◽  
pp. 249-256 ◽  
Author(s):  
FU-SHENG TSUNG ◽  
GARRISON W. COTTRELL
Keyword(s):  
Finite Difference ◽  
Time Delays ◽  
Learning Algorithm ◽  
Time Constants ◽  
Learning Time ◽  
Discrete Algorithms ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
Discrete Networks ◽  
Period Of Oscillation

A recurrent learning algorithm based on a finite difference discretization of continuous equations for neural networks is derived. This algorithm has the simplicity of discrete algorithms while retaining some essential characteristics of the continuous equations. In discrete networks learning smooth oscillations is difficult if the period of oscillation is too large. The network either grossly distorts the waveforms or is unable to learn at all. We show how the finite difference formulation can explain and overcome this problem. Formulas for learning time constants and time delays in this framework are also presented.

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