Experimental Design and Modeling for Forward-Inverse Maps

In customer-driven design of systems or products, one has performance targets in mind and would like to determine values for product or system parameters that meet such targets. Engineering computer simulation models predict performance given design parameter values; meeting a target is done iteratively through an optimization search procedure, typically by optimizing a regression, neural network or other type of approximation <i>metamodel</i> of the computer model. We pose the thesis that, since forward metamodel construction is a key part of this strategy, constructing an inverse metamodel directly is advantageous. The inverse metamodel obviates the need for optimization in many settings. One can design experiments that allow simultaneous fitting of forward and inverse metamodels. We discuss the potential for this strategy, the connection with the calibration problem, and some of the issues that must be resolved to make the approach practical.在面向客户的系统或产品设计中，设计者通常会预先设定性能目标，并希望确定能够满足该目标的产品或系统参数取值。工程计算机仿真模型可基于给定的设计参数值预测系统性能；而达成性能目标的传统流程需通过优化搜索程序迭代完成，通常会针对计算机模型的回归模型、神经网络或其他类型的近似元模型（metamodel）进行优化。本文提出如下论点：由于正向元模型构建是该设计策略的核心环节，直接构建逆向元模型将具备显著优势。在多数场景下，逆向元模型可免去优化步骤。研究者可设计实验，实现正向与逆向元模型的同步拟合。本文将探讨该策略的应用潜力、其与校准问题的关联，以及为使该方法具备实用性所需解决的若干关键问题。