A Bayesian Approach to Optimal Sequential Experimental Design using Approximate Dynamic Programming

Experimental data play an essential role in developing and refining models of physical systems. Not all experimental results are equally useful, and some experiments can be much more valuable than others. Well-chosen experiments can thus lead to substantial resource savings. Optimal experimental design seeks to quantify and maximize the value of experimental data. Common current practice for designing multiple experiments consists of suboptimal approaches: open-loop design that chooses all experiments simultaneously, and greedy design that optimally selects the next experiment without accounting for the future. In this thesis, we develop a rigorous formulation in a closed-loop dynamic programming (DP) framework that yields the true optimal sequence of experiments under the uncertainty of their results. The framework is suitable for nonlinear models and for the experimental purpose of Bayesian parameter inference. Furthermore, we develop a set of numerical tools that solve the DP design problem with particular attention to approximation methods for computationally intensive models. These tools include various methods of approximate dynamic programming, as well as numerical techniques such as polynomial surrogates and stochastic optimization that accelerate the computations. In this thesis, the superiority of the DP design is demonstrated in a simple linear-Gaussian model problem. Future work will apply the DP design framework to a realistic application problem involving optimal sensor placement in a convection-diffusion field.