Optimal statistical design for inverse problems with ordinary differential equations

Eugene Demidenko

Departments of Mathematics and Biomedical Data Science

In few words, I discuss the problem of where to make measurements of a physical system, governed by ordinary differential equations, to optimally estimate the unknown parameters. I start with a five thousand year old problem of nailing a plank to the wall as an introduction of the optimal statistical design of experiments in linear regression models. I use a five hundred year old problem of hanging wire for estimation of the sagging parameter to introduce a nonlinear optimal statistical design. Then I will switch to the heat transfer problem of finding the optimal location of the temperature sensors. The idea of the adaptive optimal design is introduced. The general formulation will follow and optimal designs with ODEs that do not admit a closed-form expression will be discussed. The talk is accessible to a wide mathematical audience including undergrads.

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