A multifidelity Bayesian optimization method for inertial confinement fusion design

TL;DR

This paper tackles the challenge of efficiently designing inertial confinement fusion experiments by addressing the problem that low- and high-fidelity simulations can have optima in different regions of parameter space. It introduces an iterative multifidelity Bayesian optimization framework based on Gaussian Process surrogates that alternates between low- and high-fidelity data to drive exploration and exploitation, respectively. Through 2D and 8D ICF design tests using HYDRA-based data and a burn-off low-fidelity surrogate, the method demonstrates faster convergence and near-optimal designs compared with high-fidelity-only approaches. The approach offers substantial computational savings and provides a principled pathway to leverage mixed fidelity information in realistic, resource-intensive design campaigns.

Abstract

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.

Figures (7)

• Figure 1: Contour plots for the 2D design example, with existing simulations as black dots. The ground truth solution (a and b) show that the optimal points for low and high fidelity are in different parts of parameter space. The algorithm alternates between selecting a pair of high and low fidelity points (c) and just additional low-fidelity points (d).
• Figure 2: Mean value contour and high-fidelity sampling at iteration 0.
• Figure 3: Mean value contour and low-fidelity sampling at iteration 0.
• Figure 4: Our multifidelity approach produces equivalent or smaller errors in both design values (top) and output yields (bottom) as a strictly high-fidelity approach. In particular, for a fixed number of high fidelity samples (horizontal axis), the additional information provided by the low fidelity samples does not increase the error and often decreases it.
• Figure 5: Histogram exhaustive sampling of HYDRA surrogate functions. The frequency counts are log-scaled. It is evident from the histograms that the low- and high-fidelity surrogates have distinct distributions of values for the same range of parameters.