Simulation-based optimal Bayesian experimental design for nonlinear systems

TL;DR

This paper introduces a Bayesian framework and algorithms for optimal experimental design in nonlinear systems, maximizing information gain from costly and complex experiments using simulation-based models.

Contribution

It presents a novel mathematical framework and computational algorithms for optimal experimental design with nonlinear simulation models, incorporating information theory and stochastic optimization.

Findings

Effective algorithms for high-dimensional optimization

Application to nonlinear combustion kinetics models

Demonstrated improved information gain in experiments

Abstract

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter estimation problems arising in detailed combustion kinetics.