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 H$\alpha$ and Ca~II 854.21 nm provide essential diagnostics of temperature, velocity, and nonthermal motions in the solar atmosphere. Multilayer spectral inversion (MLSI) offers a physically interpretable framework for modeling these lines by approximating the atmosphere with a finite number of radiative transfer layers. Although MLSI is computationally more efficient than full non-local thermodynamic equilibrium inversions, it still relies on pixel-by-pixel constrained nonlinear least-squares fitting, which becomes prohibitively expensive for large field-of-view or high-cadence imaging spectroscopic observations. In this work, we introduce a physics-informed neural network (PINN) framework to accelerate the MLSI process while preserving its analytic radiative transfer formulation. By embedding the multilayer radiative transfer constraints directly into the neural network architecture and loss function, the model learns the mapping between observed spectral profiles and MLSI parameters under explicit physical consistency. Applied to spectral data of the H$\alpha$ and Ca~II 854.21 nm lines, the proposed approach significantly reduces the computational cost of inversion while maintaining agreement with conventional MLSI results. The method enables rapid and physically guided inference of chromospheric plasma parameters from large-scale datasets. Our results demonstrate that physics-informed neural networks provide an efficient and interpretable pathway for next-generation chromospheric spectral inversion.