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<p>Physics-informed neural networks (PINNs) are vital for machine learning and exhibit significant advantages when handling complex physical problems. The PINN method can rapidly predict <sup>220</sup>Rn progeny concentration and is very important for regulating and measuring this property. To construct a PINN model, training data are typically preprocessed; however, this approach changes the physical characteristics of the data, with the preprocessed data potentially no longer directly conforming to the original physical equations. As a result, the original physical equations cannot be directly employed in the PINN. Consequently, an effective method for transforming physical equations is crucial for accurately constraining PINNs to model the <sup>220</sup>Rn progeny concentration prediction. This study presents an equation adaptation approach for neural networks, which is designed to improve prediction of <sup>220</sup>Rn progeny concentration. Five neural network models based on three architectures are established: a classical network, a physics-informed network without equation adaptation, and a physics-informed network with equation adaptation. The transport equation of the <sup>220</sup>Rn progeny concentration is transformed via equation adaption and integrated with the PINN model. The compatibility and robustness of the model with equation adaption is then analyzed. The results show that PINNs with equation adaption converge consistently with classical neural networks in terms of the training and validation loss and achieve the same level of prediction accuracy. This outcome indicates that the proposed method can be integrated into the neural network architecture. Moreover, the prediction performance of classical neural networks declines significantly when interference data are encountered, whereas the PINNs with equation adaption exhibit stable prediction accuracy. This performance demonstrates that the proposed method successfully harnesses the constraining power of physical equations, significantly enhancing the robustness of the resultant PINN models. Thus, the use of a physics-informed network with equation adaption can guarantee accurate prediction of <sup>220</sup>Rn progeny concentration.</p>

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Physics-informed neural network with equation adaption for 220Rn progeny concentration prediction

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Shao-Hua Hu,
  • Qi Qiu,
  • De-Tao Xiao,
  • Xiang-Yuan Deng,
  • Xiang-Yu Xu,
  • Peng-Hao Fan,
  • Lei Dai,
  • Zhi-Wen Hu,
  • Tao Zhu,
  • Qing-Zhi Zhou

摘要

Physics-informed neural networks (PINNs) are vital for machine learning and exhibit significant advantages when handling complex physical problems. The PINN method can rapidly predict 220Rn progeny concentration and is very important for regulating and measuring this property. To construct a PINN model, training data are typically preprocessed; however, this approach changes the physical characteristics of the data, with the preprocessed data potentially no longer directly conforming to the original physical equations. As a result, the original physical equations cannot be directly employed in the PINN. Consequently, an effective method for transforming physical equations is crucial for accurately constraining PINNs to model the 220Rn progeny concentration prediction. This study presents an equation adaptation approach for neural networks, which is designed to improve prediction of 220Rn progeny concentration. Five neural network models based on three architectures are established: a classical network, a physics-informed network without equation adaptation, and a physics-informed network with equation adaptation. The transport equation of the 220Rn progeny concentration is transformed via equation adaption and integrated with the PINN model. The compatibility and robustness of the model with equation adaption is then analyzed. The results show that PINNs with equation adaption converge consistently with classical neural networks in terms of the training and validation loss and achieve the same level of prediction accuracy. This outcome indicates that the proposed method can be integrated into the neural network architecture. Moreover, the prediction performance of classical neural networks declines significantly when interference data are encountered, whereas the PINNs with equation adaption exhibit stable prediction accuracy. This performance demonstrates that the proposed method successfully harnesses the constraining power of physical equations, significantly enhancing the robustness of the resultant PINN models. Thus, the use of a physics-informed network with equation adaption can guarantee accurate prediction of 220Rn progeny concentration.