Sequential Exploration of Complex Surfaces Using Minimum Energy Designs

A new space-filling design, called minimum energy design (MED), is proposed to explore unknown regions of the design space of particular interest to an experimenter. The key ideas involved in constructing the MED are the visualization of each design point as a charged particle inside a box, and minimization of the total potential energy of these particles. It is shown through theoretical arguments and simulations that with a proper choice of the charge function, the MED can asymptotically generate any arbitrary probability density function. A version of the MED, which adaptively updates the design by “learning” about the unknown response surface sequentially, is proposed and implemented. Two potential applications of MED in simulation of complex probability densities and optimization of complex response surfaces are discussed and demonstrated with examples. This article has supplementary material online.     

El Niño's Uneven Disruption of World's Electricity Systems

In a recent column in this journal, I discussed how in the early to middle nineteenth century Napoleon and Bismarck contributed to Europe's lack of any shale gas development compared to the shale boom in North America.¹ But that is rather recent business compared to those seventeenth-century fishermen off the coast of South America who noticed unusually warm waters that tended to occur every few years around Christmas—labelling the phenomenon El Niño.     

Distributed Energy and Low Carbon vs. Consumers,Regulators, and Tin Men

Economists, regulators, engineers, corporations, and climate activists all search for means to decarbonize the emissions footprint of the electric power industry. It is a pressing search as global electricity demand continues to grow quickly (particularly in the developing world) and fossil fuels continue to dominate generation. (See Exhibit 1 .)