Abstract:
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Space-filling designs are commonly used as experimental designs in computer experiments. For example, maximin distance designs fill the experimental region uniformly while maximizing the minimum pairwise distance among the design points. In this talk, we will show that they can be modified to follow any arbitrary distribution by appropriately assigning weights to each design point. This method has a physical analogy of minimizing the total potential energy of electrically charged particles inside a box and therefore, we call the new space-filling design as minimum energy design. We will explain how this can be used in the simulation of complex probability distributions and in the global optimization of expensive black-box functions.
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