Authors: Ziyang Zhang (NJIT), Qin Li (NJIT), Vasyl Yurchyshyn (BBSO), Kangwoo Yi (NJIT), Haimin (BBSO & NJIT), Bo Shen (NJIT)

Strong chromospheric absorption lines such as Hα and Ca II 8542 Å provide important diagnostics of plasma dynamics and thermal structure in the solar chromosphere. Multilayer spectral inversion (MLSI) offers a physically interpretable framework for modeling these lines with a finite number of radiative-transfer layers, but conventional MLSI still requires pixel-by-pixel nonlinear least-squares fitting and is therefore costly for large imaging spectroscopic data sets. In this work, we introduce a physics-informed neural-network framework to accelerate MLSI while retaining its analytic radiative-transfer formulation. The network predicts MLSI parameters from observed line profiles, and the predicted parameters are passed through the differentiable MLSI forward model to synthesize spectra. We train the model in two stages: a first stage using only the spectral reconstruction loss, followed by a second fine-tuning stage that combines spectral consistency with parameter-space supervision from conventional MLSI results for a single reference raster. This strategy reduces the need for large precomputed training sets while preserving the physical interpretability of the MLSI parameters. We apply the method to FISS Hα and Ca II 8542 Å observations of both quiet-Sun and active-region targets. The MLSI-PINN parameter maps reproduce the main spatial structures of direct MLSI inversions, show strong pixel-wise correlations for most parameters, and generate reconstructed spectra that closely match the observed profiles. These results demonstrate that a two-stage physics-informed neural network can provide a fast and physically constrained approximation to MLSI for same-day chromospheric spectral inversion.