Description
Accurate treatment of electron heat transport [1] in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. In this work, we develop a resolution-independent, data-driven heat flux closure using a neural operator framework trained on first-principles particle-in-cell (PIC) simulations [2]. A Fourier Neural Operator [3] is employed to learn the functional mapping from the electron temperature profile to the divergence of the heat flux, enabling a nonlocal closure that is independent of grid resolution. The model is trained on two representative transport problems, the relaxation of a hot spot and the Epperlein-Short temperature perturbation, spanning regimes with significant nonlocal effects. When embedded into the electron energy equation and solved implicitly [4], the learned closure accurately reproduces the spatiotemporal evolution of temperature and heat flux observed in PIC simulations, while outperforming the widely used Schurtz-Nicolaï-Busquet (SNB) [5] model. Remarkably, models trained on coarse-resolution data remain accurate when deployed within fine-resolution solvers, demonstrating strong generalization across resolutions. The learned operator enables stable and efficient iterative solutions, reducing computational cost by more than an order of magnitude relative to SNB-based solvers. These results establish a practical pathway for integrating machine-learning closures into radiation-hydrodynamic simulations and highlight the potential of neural operators as iterative solvers bridging kinetic and fluid descriptions of plasma transport.
[1] Gregori et al, Phys. Rev. Lett. 92, 205006 (2004).
[2] Fonseca et al, Comp. Sci-ICCS. 2329, 342–351 (2002).
[3] Li et al, arXiv:2010.08895 (2021).
[4] Cao et al, Phys. Plasmas 22, 082308 (2015).
[5] Schurtz et al, Phys. Plasmas 7, 4238 (2000).