Neural Message Passing for Objective-Based Uncertainty Quantification and Optimal Experimental Design

Real-world scientific or engineering applications often involve mathematical modeling of complex uncertain systems with a large number of unknown parameters. The complexity of such systems, and the enormous uncertainties therein, typically make accurate model identification from the available data infeasible. In such cases, it is desirable to represent the model uncertainty in a Bayesian paradigm, based on which we can design robust operators that maintain the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to maximally enhance the performance of such operators. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) has been shown to provide effective means for quantifying and handling uncertainty in complex systems, a major drawback has been the high computational cost of estimating MOCU. In this work, we demonstrate for the first time that one can design accurate surrogate models for efficient objective-UQ via MOCU based on a data-driven approach. We adopt a neural message passing model for surrogate modeling, which incorporates a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance the robust synchronization performance through uncertainty reduction. Through quantitative performance assessment, we show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, virtually without any visible loss of performance compared to the previous state-of-the-art. The proposed approach can be applied to general OED tasks, beyond the Kuramoto model.