Contour location$\unicode{x2014}$the process of sequentially training a surrogate model to identify the design inputs that result in a pre-specified response value from a single computer experiment$\unicode{x2014}$is a well-studied active learning problem. Here, we tackle a related but distinct problem: identifying the input configuration that returns pre-specified values of multiple independent computer experiments simultaneously. Motivated by computer experiments of the rotational torques acting upon a vehicle in flight, we aim to identify stable flight conditions which result in zero torque forces. We propose a "joint contour location" (jCL) scheme that strikes a strategic balance between exploring the multiple response surfaces while exploiting learning of the intersecting contours. We employ both shallow and deep Gaussian process surrogates, but our jCL procedure is applicable to any surrogate that can provide posterior predictive distributions. Our jCL designs significantly outperform existing (single response) CL strategies, enabling us to efficiently locate the joint contour of our motivating computer experiments.

翻译：等高线定位——通过顺序训练代理模型以识别单个计算机实验中产生预设响应值的设计输入——是一个经过深入研究的主动学习问题。本文处理一个相关但不同的问题：同时识别能够使多个独立计算机实验返回预设值的输入配置。受飞行器所受旋转扭矩计算机实验的启发，我们的目标是识别导致零扭矩力的稳定飞行条件。我们提出了一种“联合等高线定位”（jCL）方案，该方案在探索多个响应曲面与利用相交等高线学习之间实现了策略性平衡。我们采用了浅层和深层高斯过程代理模型，但我们的jCL程序适用于任何能够提供后验预测分布的代理模型。我们的jCL设计方案显著优于现有（单响应）CL策略，使我们能够高效定位激励性计算机实验的联合等高线。