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Resolution-Robust Machine Learning Heat Flux Closure for Inertial Confinement Fusion Plasmas

M. Luo1,*, A. R. Bell1,2, F. Miniati3, S. M. Vinko1, and G. Gregori1

  • 1Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 2Central Laser Facility, STFC Rutherford Appleton Laboratory, Harwell, Oxfordshire OX11 0QX, United Kingdom
  • 3Mach42, Robert Robinson Avenue, Oxford Science Park, Oxford OX4 4GP, United Kingdom

  • *Contact author: mufei.luo@physics.ox.ac.uk
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PRX Intelligence 1, 013017 – Published 3 September, 2026

DOI: https://doi.org/10.1103/9l4n-mnz6

Abstract

Accurate modeling of heat flux in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. We develop a resolution-robust machine learning heat flux closure trained on particle-in-cell simulations using a Fourier neural operator. Two nonlocal electron thermal conduction models are trained and tested. When embedded self-consistently into the electron energy equation, the learned closure faithfully reproduces the temperature evolution and shows good temporal extrapolation and generalization capability. Remarkably, models trained on coarse-resolution data accurately predict heat flux when deployed in substantially finer-resolution implicit, iterative solvers of the energy equation, significantly enhancing the practicality of embedding data-driven closures into partial differential equation solvers. These results establish a data-driven closure that bridges kinetic and fluid descriptions and provides a viable pathway for treating machine learning as an iterative solver within the radiation-hydrodynamic simulations of inertial confinement fusion plasma.

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PRX Intelligence 1, 013017– Published 3 September, 2026
  • Received 21 March 2026
  • Revised 14 June 2026
  • Accepted 30 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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