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In this paper, the optimal choice of the interior penalty parameter of thediscontinuous Galerkin finite element methods for both the elliptic problemsand the Biot's systems are studied by utilizing the neural network and machinelearning. It is crucial to choose the optimal interior penalty parameter, whichis not too small or not too large for the stability, robustness, and efficiencyof the numerical discretized solutions. Both linear regression and nonlinearartificial neural network methods are employed and compared using severalnumerical experiments to illustrate the capability of our proposedcomputational framework. This framework is an integral part of a developingautomated numerical simulation platform because it can automatically identifythe optimal interior penalty parameter. Real-time feedback could also beimplemented to update and improve model accuracy on the fly.

Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot's System by Employing Machine Learning