https://doi.org/10.1140/epjs/s11734-026-02260-8
Regular Article
A residual neural network surrogate model for fast NLTE spectral calculations in gold plasmas
1
Institute of Applied Physics and Computational Mathematics, 100088, Beijing, China
2
HEDPS, Center for Applied Physics and Technology, Peking University, 100084, Beijing, China
a
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Received:
1
January
2026
Accepted:
3
March
2026
Published online:
12
March
2026
Abstract
Non-local thermodynamic equilibrium (NLTE) spectral calculations constitute one of the dominant computational bottlenecks in inertial confinement fusion (ICF) simulations, owing to the large configuration space and the multi-scale behavior of atomic processes. To address this challenge, we develop a machine learning surrogate model that replaces the iterative collisional–radiative (CR) solver with a single forward-pass neural network. A dataset of 34,000 gold-plasma states is generated using a detailed configuration accounting model, covering wide ranges of electron temperature, particle density, and radiation-field conditions. A two-layer residual neural network with logarithmic scaling is identified as the optimal architecture through systematic hyperparameter studies. Within the training-domain temperature range of 
, the surrogate model achieves average relative errors of 
for emissivity and 
for absorptivity. The model also extrapolates reliably to high-temperature conditions (
), maintaining errors below 
. Its performance degrades at low temperatures (
), with emissivity errors increasing to 
, indicating a need for improved modeling of weakly ionized plasmas. Importantly, the surrogate model reduces the per-sample evaluation time by more than three orders of magnitude, achieving a speed-up exceeding 
compared with the CR model. Overall, the proposed surrogate model provides an accurate and efficient alternative to CR calculations, offering significant potential to accelerate integrated ICF simulations.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Yong Wu, Jianguo Wang, Rui Jin and Zeqing Wu have contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
