Enabling Fast, High-Fidelity NLTE Modeling via Reduced-Order Methods and Symbolic Dynamics Learning

Non-Local Thermodynamic Equilibrium (NLTE) modeling is critical for accurately predicting key plasma properties —such as charge state distributions, equations of state, and radiative opacity—in high-energy-density plasmas. However, existing approaches struggle to balance computational efficiency with atomic data fidelity, making it difficult to perform fast simulations that incorporate detailed atomic structure. Here, we present a data-driven framework for constructing reduced-order NLTE models that improve both fidelity and efficiency in radiation–hydrodynamics simulations to address this challenge. Starting from high-fidelity atomic state population data generated under laser–plasma conditions, we apply a data-driven dimensionality reduction technique—autoencoders—to compress thousands of atomic states into a small set of latent variables that capture most of the population variance. The time evolution of these latent variables is then modeled using symbolic regression techniques to extract governing equations directly from the data, enhancing both interpretability and generalization. Its scalability across elements and plasma regimes paves the way for fast, interpretable, and high-fidelity NLTE surrogates for short-pulse laser, X-ray laser, and inertial confinement fusion (ICF) applications.