Multi-level binary replacement (MBR) design for computer experiments in high-dimensional nonlinear systems



Computer experiments are useful for studying a complex system, e.g. a high-dimensional nonlinear mathematical model of a biological or physical system. Based on the simulation results, an empirical “metamodel” may then be developed, emulating the behavior of the model in a way that is faster to compute and easier to understand. In modelometrics, the model phenome of a computer model is recorded, once and for all, by structured simulations according to a factorial design in the model inputs, and with high-dimensional profiling of its simulation outputs. A multivariate metamodel is then developed, by multivariate analysis of the input–output data, akin to how high-dimensional data are analyzed in chemometrics. To reveal strongly nonlinear input–output relationships, the factorial design must probe the design space at many different levels for each of the many input factors. A reduced factorial design method may be required if combinatorial explosion is to be avoided. In the multi-level binary replacement (MBR) design the levels of each input factor are represented as binary numbers, and all the individual binary factor bits are then combined in a fractional factorial (FF) design. The experiment size can thereby be greatly reduced at the price of some binary confounding. The MBR method is here described and then illustrated for the optimization of a nonlinear model of a microbiological growth curve with five design factors, for finding the relevant region in the design space, and subsequently for estimating the optimal design points in that space. Copyright © 2010 John Wiley & Sons, Ltd.