Optimal experimental design (OED) has far-reaching impacts in many scientific domains. We study OED over a continuous-valued design space, a setting that occurs often in practice. Optimization of a distributional function over an infinite-dimensional probability measure space is conceptually distinct from the discrete OED tasks that are conventionally tackled. We propose techniques based on optimal transport and Wasserstein gradient flow. A practical computational approach is derived from the Monte Carlo simulation, which transforms the infinite-dimensional optimization problem to a finite-dimensional problem over Euclidean space, to which gradient descent can be applied. We discuss first-order criticality and study the convexity properties of the OED objective. We apply our algorithm to the tomography inverse problem, where the solution reveals optimal sensor placements for imaging.

翻译：最优实验设计（OED）在众多科学领域具有深远影响。本文研究连续值设计空间上的OED问题——这一设定在实践中频繁出现。在无限维概率测度空间上优化分布函数，其概念性框架与常规处理的离散OED任务存在本质差异。我们提出基于最优传输与Wasserstein梯度流的技术方法。通过蒙特卡洛模拟导出一套实用计算方案，该方案将无限维优化问题转化为欧氏空间上的有限维问题，从而可应用梯度下降法求解。本文讨论一阶临界性并探究OED目标函数的凸性性质。我们将所提算法应用于层析成像反问题，其解揭示了成像的最优传感器配置方案。