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We present a reduced order modeling (ROM) technique for subsurfacemulti-phase flow problems building on the recently introduced deep residualrecurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrentneural network for modeling the evolution of dynamical systems. The DR-RNNarchitecture is inspired by iterative update techniques of line search methodswhere a fixed number of layers are stacked together to minimize the residual(or reduced residual) of the physical model under consideration. In thismanuscript, we combine DR-RNN with proper orthogonal decomposition (POD) anddiscrete empirical interpolation method (DEIM) to reduce the computationalcomplexity associated with high-fidelity numerical simulations. In thepresented formulation, POD is used to construct an optimal set of reduced basisfunctions and DEIM is employed to evaluate the nonlinear terms independent ofthe full-order model size.  We demonstrate the proposed reduced model on two uncertainty quantificationtest cases using Monte-Carlo simulation of subsurface flow with randompermeability field. The obtained results demonstrate that DR-RNN combined withPOD-DEIM provides an accurate and stable reduced model with a fixedcomputational budget that is much less than the computational cost of standardPOD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems.

Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks