Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. We abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate optimal control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated log-predictive likelihood of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

翻译：现代先进制造与先进材料设计通常需要搜索相对高维的过程控制参数空间，以寻找能使结构、性能与表现参数达到最优的设置。从控制参数到设计参数的映射关系必须通过含噪实验或昂贵仿真来确定。我们将该问题抽象为一个数学框架：需通过含噪测量确定从控制空间到设计空间的未知函数，从而在指定容差范围内定位能生成期望设计特征的最优控制设置，并量化不确定性。我们提出目标导向自适应设计（TAD）算法，该算法能高效完成这一采样任务。TAD在每次迭代中构建未知映射的高斯过程代理模型，提出新的控制设置批次进行实验采样，并优化目标设计的更新对数预测似然。当定位到的解的不确定性落在容差框内时，TAD即停止；或通过衡量预期未来信息量判定搜索空间已被穷尽而无解。TAD以类似但本质上不同于贝叶斯优化与最优实验设计的方式，体现了探索-利用的平衡机制。