Data underlying the study on 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.

原子能级跃迁的精准预测对于量子光谱学、量子器件优化以及原子动力学研究的发展至关重要。传统方法往往面临计算成本高昂或物理可解释性有限等挑战。为克服上述局限，研究人员提出了物理感知双向长短期记忆网络（Physics-Informed Bi-LSTM，PINN-Bi-LSTM）模型。该框架将双向长短期记忆网络（Bidirectional Long Short-Term Memory, Bi-LSTM）与物理感知神经网络（Physics-Informed Neural Networks, PINNs）相结合：双向长短期记忆网络模块可从时序数据（如光谱发射记录）中捕捉原子态演化的时序模式，而物理感知神经网络模块则通过基于物理原理的损失项，强制执行量子力学约束（如能量守恒、跃迁概率规则）。研究人员采用合成数据集与实验数据集对该模型进行了验证，并与包括从头算模拟、独立式双向长短期记忆网络以及长短期记忆网络-自回归移动平均混合模型在内的基准方法展开对比。实验结果表明，相较于传统方法，PINN-Bi-LSTM模型实现了更优的预测精度（0.92）、更低的均方误差（0.01），且对复杂系统（如多电子原子、动态受扰态）具备更强的泛化能力。此外，该模型在含噪或稀疏数据集上仍可保持稳定的性能，这得益于其兼顾数据效率与物理严谨性的双重设计思路。本研究将时序建模能力与基础物理原理相结合，推动了量子态预测领域的发展，可为实时光谱学与量子器件优化提供应用场景。