Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

A simulation tool capable of speeding up the calculation for linear poroelasticity problems in heterogeneous porous media is large practical interest engineers, particular, to effectively perform sensitivity analyses, uncertainty quantification, optimization, or control operations on fluid pressure and bulk deformation fields. Towards this goal, we present here a non-intrusive model reduction framework using proper orthogonal decomposition (POD) neural networks based usual offline-online paradigm. As conductivity can be highly span several orders magnitude, utilize interior penalty discontinuous Galerkin (DG) method as full order solver handle discontinuity ensure local mass conservation during offline stage. We then use POD data compression compare nested technique, which time uncertain parameter domains are compressed consecutively, classical all simultaneously. The finally trained map set parameters, could correspond material properties, boundary conditions, geometric characteristics, collection coefficients calculated from an $$L^2$$ projection over reduced basis. evaluation obtain corresponding new values parameters online show that our provides reasonable approximations DG solution, but it significantly faster. Moreover, capture sharp discontinuities both displacement fields resulting heterogeneity conductivity, generally challenging intrusive methods. sources error presented, showing technique computationally advantageous still comparable accuracy method. also explore effect different choices hyperparameters network performance.