Optimum Experimental Design for Interface Identification Problems

TL;DR

This paper develops an optimal experimental design framework for accurately identifying interfaces in diffusion processes, leveraging shape manifold structures and sensor activation patterns to enhance estimation precision.

Contribution

It introduces a novel OED formulation for shape-based interface identification problems, incorporating shape manifold structures and sensor activation strategies.

Findings

Numerical results demonstrate improved estimation accuracy.

The simplicial decomposition algorithm effectively solves the OED problem.

Optimal sensor activation patterns enhance interface identifiability.

Abstract

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.