Young (and some not-so-young) researchers often wonder how to extract good research ideas and develop useful methodologies from solving real world problems. The path is rarely straightforward and its success depends on the circumstances, tenacity and luck. I will use three examples to illustrate how I trod the path. The first involved an attempt to find optimal growth conditions for nano structures (i.e., wires, belts, saws). It led to the development of a new method “sequential minimum energy design (smed)”, which exploits an analogy to potential energy of charged particles. After a few years of frustrated efforts and relentless pursuit, we realized that smed is more suitable for generating samples adaptively to mimic an arbitrary distribution rather than for optimization. The main objective of the second example was to build an efficient statistical emulator based on finite element simulation results with two mesh densities in cast foundry operations. It eventually led to the development of a class of nonstationary Gaussian process models that can be used to connect simulation data of different precisions and speeds. The third example hails from cell biology. In a T cell adhesion experiment at Georgia Tech, the biologist was not satisfied with the use of graphical method to understand the serial dependency of cell adhesion over repeated trials. It led to the development of hidden Markov models with new features that reflect the nature of the experiment. In each example, the developed methodology has broader applications beyond the original problem. I will explain the thought process in each example but cannot promise any general observation.
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