无需梯度信息，用粒子系统实现高效实验设计。
Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems
- 结合粒子优化与采样方法，不依赖梯度进行实验设计。
- 提出变分高斯与参数化拉普拉斯近似，有效估算信息增益。
- 适用于高维与偏微分方程约束问题，适合复杂系统研究者。
我们提出一种无梯度的贝叶斯最优实验设计（BOED）框架，适用于梯度信息缺失的复杂系统。方法结合基于粒子的集成卡尔曼反演（EKI）用于设计优化，以及仿射不变朗之万动力学（ALDI）采样器实现高效后验采样，两者均无需梯度且基于粒子集。为解决BOED中嵌套期望带来的计算挑战，我们引入变分高斯和参数化拉普拉斯近似，提供期望信息增益（EIG）的可计算上下界。这些近似使高维空间和偏微分方程约束反问题中的效用估计具备可扩展性。通过线性高斯模型到基于偏微分方程的推断任务等数值实验，验证了该框架在信息驱动实验设计中的鲁棒性、准确性和效率。
原文摘要 · Abstract (English)
We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.
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