Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace complex computer codes. Some sequential design strategies can be understood within the Stepwise Uncertainty Reduction (SUR) framework. In the SUR framework, each new design point is chosen by minimizing the expectation of a metric of uncertainty with respect to the yet unknown new data point. These methods offer an accessible framework for sequential experiment design, including almost sure convergence for common uncertainty functionals. This paper introduces two strategies. The first one, entitled Constraint Set Query (CSQ) is adapted from D-optimal designs where the search space is constrained in a ball for the Mahalanobis distance around the maximum a posteriori. The second, known as the IP-SUR (Inverse Problem SUR) strategy, uses a weighted-integrated mean squared prediction error as the uncertainty metric and is derived from SUR methods. It is tractable for Gaussian process surrogates with continuous sample paths. It comes with a theoretical guarantee for the almost sure convergence of the uncertainty functional. The premises of this work are highlighted in various test cases, in which these two strategies are compared to other sequential designs.

翻译：序贯设计是主动学习领域中一个高度活跃的研究方向，它为在有限计算资源下设计计算机实验提供了通用框架。其核心目标是构建高效的代理模型以替代复杂的计算机程序。部分序贯设计策略可在逐步不确定性缩减框架下得到合理解释。在该框架中，每个新设计点的选择通过最小化关于未知新数据点的不确定性度量期望值来实现。这些方法为序贯实验设计提供了可行的理论框架，包括对常见不确定性泛函的几乎必然收敛性保证。本文提出两种策略：第一种名为约束集查询，改编自D-最优设计方法，其搜索空间被约束在马哈拉诺比斯距离后验最大值的球域内；第二种称为反问题逐步不确定性缩减策略，采用加权积分均方预测误差作为不确定性度量，源自逐步不确定性缩减方法体系。该策略适用于具有连续样本路径的高斯过程代理模型，并附有不确定性泛函几乎必然收敛的理论保证。本文通过多个测试案例凸显了这两种策略的优越性，并将其与其他序贯设计方法进行了对比分析。