  Due to their cost, experiments for inertial confinement fusion (ICF) heavily
rely on numerical simulations to guide design. As simulation technology
progresses, so too can the fidelity of models used to plan for new experiments.
However, these high-fidelity models are by themselves insufficient for optimal
experimental design, because their computational cost remains too high to
efficiently and effectively explore the numerous parameters required to
describe a typical experiment. Traditionally, ICF design has relied on
low-fidelity modeling to initially identify potentially interesting design
regions, which are then subsequently explored via selected high-fidelity
modeling. In this paper, we demonstrate that this two-step approach can be
insufficient: even for simple design problems, a two-step optimization strategy
can lead high-fidelity searching towards incorrect regions and consequently
waste computational resources on parameter regimes far away from the true
optimal solution. We reveal that a primary cause of this behavior in ICF design
problems is the presence of low-fidelity optima in distinct regions of the
parameter space from high-fidelity optima. To address this issue, we propose an
iterative multifidelity Bayesian optimization method based on Gaussian Process
Regression that leverages both low- and high-fidelity modelings. We
demonstrate, using both two- and eight-dimensional ICF test problems, that our
algorithm can effectively utilize low-fidelity modeling for exploration, while
automatically refining promising designs with high-fidelity models. This
approach proves to be more efficient than relying solely on high-fidelity
modeling for optimization.
