The representer method for state and parameter estimation in single-phase Darcy flow

The objective of this paper is to study the representer method for the inverse problem of combined parameter and state estimation in single-phase Darcy flow in porous media. A variational formulation is posed for the generalized inverse problem in the sense of weighted least-squares. An iterative representer-based algorithm is derived to approximate the Euler–Lagrange equations. It is proved that the linearized problem can be solved exactly by an extension of the representer method which inherits the same well-known properties of this technique. Implementation of the numerical algorithm for synthetic numerical experiments shows improved estimates of the poorly known prior guess.