Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data

TL;DR

This paper introduces a Bayesian experimental design method that improves computational efficiency by reformulating utility expectations and employing conditional density estimation, enabling more effective decision-making in costly and complex experiments.

Contribution

It presents a novel approach that reformulates utility calculations and uses conditional density estimation to accelerate Bayesian optimal experimental design.

Findings

Significantly improves numerical efficiency of utility expectation computation.

Effectively identifies informative datasets during model fitting.

Validates approach through theoretical analysis and practical applications.

Abstract

The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we explore optimal experimental design within a Bayesian framework, utilizing Bayes' theorem to reformulate the utility expectation--originally expressed as a nested double integral--into an independent double integral form, significantly improving numerical efficiency. To further accelerate the computation of the proposed utility expectation, conditional density estimation is employed to approximate the ratio of two Gaussian random fields, while covariance serves as a selection criterion to identify informative datasets during model fitting and integral evaluation. In scenarios characterized by low simulation efficiency and high costs of raw data acquisition, key challenges such as surrogate modeling, failure probability estimation, and parameter inference are systematically restructured within the Bayesian experimental design framework. The effectiveness of the proposed methodology is validated through both theoretical analysis and practical applications, demonstrating its potential for enhancing experimental efficiency and decision-making under uncertainty.