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

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.