Reduced-order optimal control of water flooding using proper orthogonal decomposition

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A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems (2019, background): “A variety of POD-based ROMs, in which the state variables and the system of equations are projected into low-dimensional space and then solved, have been applied for a range of subsurface flow problems [1, 2, 3, 4, 5].”
A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models (2014, methodology): “In order to determine the value of l, an ‘energy’ criterion is often applied, as described in Sarma et al. (2008) and van Doren et al. (2006).”
Use of reduced-order models in well control optimization (2017, methodology): “Van Doren et al. (2006) applied this approach to adjoint-based optimization of water flooding.”
Constraint reduction procedures for reduced‐order subsurface flow models based on POD–TPWL (2015, methodology): “Specifically, for reservoir simulation problems, speedup factors of at most 10 have been achieved using this approach [6, 7].”
A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation (2008, methodology): “Such an approach may result in significant computational savings when Galerkin-type numerical schemes are implemented (Ravindran 2002; Kunisch and Volkwein 1999) or an implicit time integration scheme to finite-difference/finite-volume semidiscretization is considered (van Doren et al. 2006).”