Experimental data play a crucial role in developing and refining models of physical systems. However, some experiments produce more useful data than others, and well-chosen experiments can provide substantial resource savings. Optimal experimental design (OED) thus seeks to systematically quantify and maximize the value of experiments. We introduce general mathematical frameworks and algorithmic approaches for OED with nonlinear models. The formalism employs Bayesian statistics and an information-theoretic objective, and rigorously defines the conditions under which batch experiments (experiments chosen simultaneously) and sequential experiments (forward-looking designs with data feedback) are truly optimal. Finding these optimal designs using conventional means is generally intractable. We develop practical numerical methods for OED by advancing computational techniques on several fronts, including stochastic optimization, polynomial chaos surrogate modeling, approximate dynamic programming, and transport maps. Using the overall algorithm, we design combustion experiments for optimal learning of Arrhenius kinetic parameters, and sequential sensor placement for contaminant source inversion.

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This is a talk of potential interest to the MICDE community. The speakers in this seminar series are Faculty Candidates in the department of Mechanical Engineering for a Computational Science search that is being carried out with the active engagement of MICDE. We expect that the successful candidate will be a highly engaged affiliate of MICDE.