A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems. (December 2017) - Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe
Highlights: Adjoint state calculations facilitate inversion of highly parameterized problems. The continuous adjoint state is differentiable for all types of model parameter. Continuous and discrete adjoint states perform similarly in regard to flow inversion. The non-intrusive character of continuous adjoint states favors implementations. Abstract: Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.