Optimum Experimental Design for Interface Identification Problems
This work addresses the challenge of optimally designing experiments for interface identification in diffusion processes, which is relevant for inverse problems in engineering and geophysics.
The paper formulates an optimum experimental design problem for identifying the interface of an inclusion in a diffusion process, using sensor activation patterns to improve estimation precision. Numerical results demonstrate the approach via a simplicial decomposition algorithm.
The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bears the structure of a shape manifold. A corresponding optimum experimental design (OED) problem is formulated in which the activation pattern of an array of sensors in space and time serves as experimental condition. The goal is to improve the estimation precision within a certain subspace of the infinite dimensional tangent space of shape variations to the manifold, and to find those shape variations of best and worst identifiability. Numerical results for the OED problem obtained by a simplicial decomposition algorithm are presented.