We propose a novel approach for sequential optimal experimental design (sOED) for Bayesian inverse problems involving expensive models with large-dimensional unknown parameters. The focus of this work is on designs that maximize the expected information gain (EIG) from prior to posterior, which is a computationally challenging task in the non-Gaussian setting. This challenge is amplified in sOED, as the incremental expected information gain (iEIG) must be approximated multiple times in distinct stages, with both prior and posterior distributions often being intractable. To address this, we derive a derivative-based upper bound for the iEIG, which not only guides design placement but also enables the construction of projectors onto likelihood-informed subspaces, facilitating parameter dimension reduction. By combining this approach with conditional measure transport maps for the sequence of posteriors, we develop a unified framework for sOED, together with amortized inference, scalable to high- and infinite-dimensional problems. Numerical experiments for two inverse problems governed by partial differential equations (PDEs) demonstrate the effectiveness of designs that maximize our proposed upper bound.

翻译：本文提出了一种新颖的序贯最优实验设计方法，用于处理涉及高维未知参数和昂贵计算模型的贝叶斯反问题。本工作的核心在于设计能够最大化从先验分布到后验分布的期望信息增益的方案，这在非高斯设定下是一项计算极具挑战性的任务。这一挑战在序贯最优实验设计中尤为突出，因为增量期望信息增益需要在不同的阶段多次近似计算，且先验分布与后验分布通常难以解析处理。为解决此问题，我们推导了增量期望信息增益的基于导数的上界，该上界不仅能指导实验设计的布局，还能构建投影算子至似然信息子空间，从而实现参数维度的有效约简。通过将此方法与针对序贯后验分布的条件测度传输映射相结合，我们建立了一个统一的序贯最优实验设计框架，并实现了摊销推断，使其能够扩展至高维乃至无限维问题。针对两个由偏微分方程控制的反问题进行的数值实验表明，最大化我们所提出上界的设计方案具有显著的有效性。