65 / 2025-03-10 09:47:53

Accelerating NLTE Calculations in ICF Using Machine Learning Surrogate Models

NLTE,ICF,Machine Learning

Accelerating NLTE Calculations in ICF Using Machine Learning Surrogate Models

Mingye Yang,¹ Jingsong Zhang,¹ Yong Wu,¹ Jianguo Wang,¹ Zeqing Wu,<sup>1,*

1</sup> Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

^*wu_zeqing@iapcm.ac.cn

In the reserach of inertial confinement fusion (ICF), the computational complexity of non-local thermodynamic equilibrium (NLTE) models significantly limits simulation efficiency. This study proposes a neural network surrogate model to accelerate NLTE spectral property calculations in gold plasmas. Firstly, a dataset consisting of  NLTE spectra for about 34,000 plasma conditions of gold plasmas is constructed using a Collisional-Radiative model. The atomic model employed was a reduced detailed configuration accounting (DCA) model. Then a residual network (ResNet) architecture with two hidden layers was employed to handle multi-scale physical quantities, such as emission coefficient and absorption coefficient. The result shows that the surrogate model  reproduces the spectra of the NLTE gold plasma excellently in the moderate- and high-temperature regimes (12–204 a.u.). The  mean relative errors for the cluster emission, absorption, and stimulated emission coefficients are 0.87%, 0.95% and 0.90%, respectively. Additionally, the model exhibited good extrapolation ability in the ultra-high-temperature regime (>204 a.u.), with errors of 1.29%, 1.84% and 2.28%, for the cluster emission, absorption, and stimulated emission coefficients, respectively. However, predictive accuracy deteriorated in the low-temperature regime (<13 a.u.), particularly for the emission coefficient, which underscores the difficulties induced by data sparsity.

By optimizing the neural network architecture and data preprocessing methods, such as applying logarithmic scaling, the study improved both training efficiency and prediction accuracy. The surrogate model reproduces spectra for NLTE gold plasmas with high accuarcy in the high-temperature range. Since the suurogate model decrease the calculation time significantly, it could be used in ICF simulations instead of the NLTE atomic model in the future. However, the generalization performance of the model in the low temperature range was still suboptimal, indicating that future work should focus on enhancing the model’s capabilities in this regime, such as by augmenting low-temperature data or incorporating physics-informed loss functions.

This study validates the potential of machine learning surrogate models in accelerating ICF simulations and outlines future directions for improving the model's performance, particularly in the low-temperature regime.