  Recent advances in objective-based uncertainty quantification (objective-UQ)
have shown that such a goal-driven approach for quantifying model uncertainty
is extremely useful in real-world problems that aim at achieving specific
objectives based on complex uncertain systems. Central to this objective-UQ is
the concept of mean objective cost of uncertainty (MOCU), which provides
effective means of quantifying the impact of uncertainty on the operational
goals at hand. MOCU is especially useful for optimal experimental design (OED)
as the potential efficacy of an experimental (or data acquisition) campaign can
be quantified by estimating the MOCU that is expected to remain after the
campaign. However, MOCU-based OED tends to be computationally expensive, which
limits its practical applicability. In this paper, we propose a novel machine
learning (ML) scheme that can significantly accelerate MOCU computation and
expedite MOCU-based experimental design. The main idea is to use an ML model to
efficiently search for the optimal robust operator under model uncertainty, a
necessary step for computing MOCU. We apply the proposed ML-based OED
acceleration scheme to design experiments aimed at optimally enhancing the
control performance of uncertain Kuramoto oscillator models. Our results show
that the proposed scheme results in up to 154-fold speed improvement without
any degradation of the OED performance.
