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摘要: 激光器中的反应动力学常包含大量激发态物种。激发态物种之间的相互作用与由此导致的数值刚性是激光器数值模拟的一大挑战。通过神经网络建立激发态反应动力学关系回归可有效降低计算复杂度，为更加准确精细的激光器数值模拟提供可能。但激发态反应动力学的复杂性同样要求神经网络具有较强的回归性能。本研究引入了序列神经网络来在较低参数量的前提下提升网络复杂回归的能力，同时提出了统计网络框架来进一步增加网络输出的多样性。所提出的方法在包含16个物种和137个反应的氟化氢振动态反应机理中进行了验证。在验证过程中，同时发现了随机性对网络性能的影响。Abstract:
Background The reaction kinetics in lasers often involves a lots of excited state species. The mutual effects and numerical stiffness arising from the excited state species pose significant challenges in numerical simulations of lasers. The development of artificial intelligence has made Neural Networks (NNs) a promising approach to address the computational intensity and instability in Excited State Reaction Kinetics (ESRK).Purpose However, the complexity of ESRK poses challenges for NN training. These reactions involve numerous species and mutual effects, resulting in a high-dimensional variable space. This demands that the NN possess the capability to establish complex mapping relationships. Moreover, the significant change in state before and after the reaction leads to a broad variable space coverage, which amplifies the demand for NN's accuracy.Methods To address the aforementioned challenges, this study introduces the successful sequence-to-sequence learning from large language learning into ESRK to enhance prediction accuracy in complex, high-dimensional regression. Additionally, a statistical regularization method is proposed to improve the diversity of the outputs. NNs with different architectures were trained using randomly sampled data, and their capabilities were compared and analyzed.Results The proposed method is validated using a vibrational reaction mechanism for hydrogen fluoride, which involves 16 species and 137 reactions. The results demonstrate that the sequential model achieves lower training loss and relative error during training. Furthermore, experiments with different hyperparameters reveal that variation in the random seed can significantly impact model performance.Conclusions In this work, the introduction of the sequential model successfully reduced the parameter count of the conventional wide model without compromising accuracy. However, due to the intrinsic complexity of ESRK, there remains considerable room for improvement in NN-based regression tasks for this domain.-
Key words:
- excited state /
- reaction kinetics /
- sequence-to-sequence learning /
- complexity
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Figure 5. The relative errors of neural networks with different constant in regularization
Figure 6. The mean square relative errors on test data of neural networks trained with another random seed
Figure 7. The relative errors on random sampling data of neural networks trained with another random seed
Figure 8. The relative errors of different constant regularized neural networks trained with another random seed
Table 1. The ranges of flow states as the neural network’s inputs
name T / K P / pa $ {Y}_{{{\mathrm{H}}_{2}}} $ $ {Y}_{{{\mathrm{H}}_{2}}\left(1\right)} $ $ {Y}_{\mathrm{H}} $ $ {Y}_{{{\mathrm{F}}_{2}}} $ $ {Y}_{\mathrm{F}} $ $ {Y}_{\text{DF}} $ $ {Y}_{\text{HF}\left(0\right)} $ lower limit $ 3.0\times {10}^{1} $ $ 1.0\times {10}^{2} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ upper limit $ 1.0\times {10}^{3} $ $ 3.5\times {10}^{3} $ $ 5.0\times {10}^{-1} $ $ 5.0\times {10}^{-3} $ $ 1.2\times {10}^{-2} $ $ 3.0\times {10}^{-3} $ $ 3.0\times {10}^{-1} $ $ 5.0\times {10}^{-1} $ $ 2.0\times {10}^{-1} $ name $ {Y}_{\text{HF}\left(1\right)} $ $ {Y}_{\text{HF}\left(2\right)} $ $ {Y}_{\text{HF}\left(3\right)} $ $ {Y}_{\text{HF}\left(4\right)} $ $ {Y}_{\text{HF}\left(5\right)} $ $ {Y}_{\text{HF}\left(6\right)} $ $ {Y}_{\text{HF}\left(7\right)} $ $ {Y}_{\text{He}} $ $ {Y}_{{{\mathrm{N}}_{2}}} $ lower limit $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ $ 0.0\times {10}^{0} $ upper limit $ 7.5\times {10}^{-2} $ $ 1.5\times {10}^{-1} $ $ 4.0\times {10}^{-2} $ $ 3.0\times {10}^{-4} $ $ 2.0\times {10}^{-4} $ $ 1.5\times {10}^{-4} $ $ 1.0\times {10}^{-4} $ $ 9.0\times {10}^{-1} $ $ 2.0\times {10}^{-1} $ 
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Table 2. The configurations of different neural networks
name structure loss total parameters Seq Serial decoders MAE 57631 SeqStd Serial decoders MAE+C 57631 Wide Parallel decoders MAE 467167 WideStd Parallel decoders MAE+C 467167
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