We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the parameter-to-observable (PtO) map is expensive to evaluate, the parameters are high-dimensional, and the optimization for sensor selection is combinatorial and high-dimensional. To address these challenges, we develop an accurate, scalable, and efficient computational framework based on derivative-informed neural operators (DINOs). The derivative of the PtO map is essential for accurate evaluation of the optimality criteria of OED in our consideration. We take the key advantage of DINOs, a class of neural operators trained with derivative information, to achieve high approximate accuracy of not only the PtO map but also, more importantly, its derivative. Moreover, we develop scalable and efficient computation of the optimality criteria based on DINOs and propose a modified swapping greedy algorithm for its optimization. We demonstrate that the proposed method is scalable to preserve the accuracy for increasing parameter dimensions and achieves high computational efficiency, with an over 1000x speedup accounting for both offline construction and online evaluation costs, compared to high-fidelity Bayesian OED solutions for a three-dimensional nonlinear convection-diffusion-reaction example with tens of thousands of parameters.

翻译：我们考虑在贝叶斯框架下，通过选择最具信息量的观测传感器来估计模型参数的最优实验设计（OED）问题。当参数到可观测（PtO）映射的评估成本高昂、参数维度高且传感器选择的优化问题具有组合性与高维性时，此类问题在计算上极为困难。为应对这些挑战，我们提出了一种基于导数信息神经算子（DINOs）的精确、可扩展且高效的计算框架。PtO映射的导数对于准确评估我们考虑的OED最优性准则至关重要。我们充分利用DINOs（一类使用导数信息训练的神经算子）的关键优势，不仅实现了PtO映射的高精度逼近，更重要的是实现了其导数的高精度逼近。此外，我们基于DINOs开发了可扩展且高效的最优性准则计算方法，并提出了一种改进的交换贪婪算法用于优化。我们证明，所提出的方法具有可扩展性，能在参数维度增加时保持精度，并实现了高计算效率——以包含数万个参数的三维非线性对流-扩散-反应示例为例，与高保真度贝叶斯OED解决方案相比，该方法在离线构建和在线评估成本方面实现了超过1000倍的加速。