Optimal experimental design of ill-posed problems: The METER approach

Abstract:
With modern measurement techniques it has become possible to extract unknown functional dependencies directly from the data. The underlying inverse problems, however, are much more demanding than standard parameter estimation. Still, systematic strategies for experimental design of these generally ill-posed problems are missing. An optimal experimental design criterion for ill-posed problems is proposed in this work. It is based on the minimization of the expected total error (abbreviated as METER) between true and estimated function. Thereby, the sound integration of the bias–variance trade-off critical to the solution of ill-posed problems is achieved. While standard optimal experimental design criteria are shown to give even qualitatively wrong predictions METER designs prove to be robust and sound. The approach is introduced for linear problems and exemplified in case studies from reaction kinetics and particle sizing by light scattering.

Keywords:
Experimental design; Inverse problem; Parameter estimation; Reaction kinetics; Numerical differentiation; Robustness; Light scattering

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