Gaussian Processes for the Design and Optimization of the Cylindrical Implosion Platform

Abstract

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this body of work, we apply surrogate modeling and optimization techniques to design studies of the cylindrical implosion platform, which provides a method for diagnosing hydrodynamic instability growth in the high-energy-density regime. Cylindrical targets allow for direct diagnostic access to the instability while preserving the effects of a convergent geometry. By enabling direct measurements of instability growth to be coupled with empirical data on thermonuclear burn, this platform provides a valuable tool for improving our understanding of the complex interplay between mix and burn. Previous studies relied upon xRAGE, Los Alamos’s Eulerian radiation hydrodynamics code, to model this class of implosions. However, full radiation hydrodynamic simulations entail significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies, thus motivating the development of machine learning models. We will investigate how these models generate predictions and their ability to measure and represent uncertainty. We will demonstrate how past work, which focused on the optimization of Gaussian process surrogates trained exclusively on output from 1D xRAGE simulations, revealed that optimal designs selected in this manner exhibited a substantial loss in yield when simulated in 2D. Despite their lower prediction accuracy, 1D simulations are less expensive than their 2D counterparts. To improve the predictive performance of the surrogate while maintaining low costs, we introduce a cost-aware multi-fidelity optimization algorithm which integrates data from 1D and 2D simulations to identify target designs that maximize yield. The design selected by the algorithm is discussed, emphasizing the design choices and implosion physics responsible for the target’s improved performance.