Inferring arbitrary quantities of interest (QoI) using limited computational or, in realistic scenarios, financial budgets, is a challenging problem that requires sophisticated strategies for the optimal allocation of the available resources. Bayesian optimal experimental design identifies the optimal set of design locations for the purpose of solving a parameter inference problem and the optimality criterion is typically associated with maximizing the worth of information in the experimental measurements. Sequential design strategies further identify the optimal design in a sequential manner, starting from a initial budget and iteratively selecting new optimal points until either an accuracy threshold is reached, or a cost limit is exceeded. In this paper, we present a generic sequential Bayesian experimental design framework that relies on maximizing an information theoretic design criterion, namely the Expected Information Gain, in order to infer QoIs formed as nonlinear operators acting on black-box functions. Our framework relies on modeling the underlying response function using non-stationary Gaussian Processes, thus enabling efficient sampling from the QoI in order to provide Monte Carlo estimators for the design criterion. We demonstrate the performance of our method on an engineering problem of steel wire manufacturing and compare it with two classic approaches: uncertainty sampling and expected improvement.

使用有限的计算或在现实场景中的财务预算来推断任意数量的兴趣 (QoI) 是一个具有挑战性的问题，需要复杂的策略来优化可用资源的分配。贝叶斯最优实验设计确定最优设计位置集，以解决参数推理问题和最优准则通常与最大化实验测量中的信息价值有关。顺序设计策略进一步以顺序方式确定最佳设计，从初始预算开始并迭代地选择新的最佳点，直到达到准确度阈值或超过成本限制。在本文中，我们提出了一个通用的顺序贝叶斯实验设计框架，该框架依赖于最大化信息论设计标准，即预期信息增益，以推断作为非线性算子形成的 QoI作用于黑盒函数。我们的框架依赖于使用非平稳高斯过程对底层响应函数进行建模，从而能够从 QoI 中进行有效采样，以便为设计标准提供 Monte Carlo 估计量。我们展示了我们的方法在钢丝制造工程问题上的性能，并将其与两种经典方法进行了比较：不确定性抽样和预期改进。