Reinforcing Prediction of Atomic Energy Level Transitions with Optimized PINN-Bi-LSTM

Accurate prediction of atomic energy level transitions is essential for advancements in quantum spectroscopy, quantum device optimization, and atomic dynamics research. Traditional methods often encounter challenges such as high computational cost or limited physical interpretability. To overcome these limitations, the Physics-Informed Bi-LSTM (PINN-Bi-LSTM) model was proposed. This framework integrates Bidirectional Long Short-Term Memory (Bi-LSTM) networks with Physics-Informed Neural Networks (PINNs). The Bi-LSTM component captures temporal patterns in atomic state evolution from time-series data (e.g., spectral emission records), while the PINN component enforces quantum mechanical constraints (e.g., energy conservation, transition probability rules) through a physics-based loss term. The model was validated using both synthetic and experimental datasets and compared against benchmark methods, including ab initio simulations, standalone Bi-LSTMs, and LSTM–ARIMA hybrids. Results demonstrated that the PINN-Bi-LSTM model achieved superior accuracy (0.92), lower mean squared error (0.01), and stronger generalizability to complex systems (e.g., multi-electron atoms, dynamically perturbed states) compared to conventional approaches. Furthermore, the model maintained robust performance in noisy or sparse datasets, attributed to its dual emphasis on data efficiency and physical rigor. This work advances quantum state prediction by unifying temporal modeling capabilities with fundamental physics, offering applications in real-time spectroscopy and quantum device optimization.