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<p>Conventional Physics-Informed Neural Networks (PINNs) with fully connected architectures have shown potential in solving differential equations, yet their inherent spectral bias limits accurate reconstruction of high-frequency components—critical for structural dynamics under broadband earthquake excitations. To overcome this limitation, we propose a Natural Frequency-Based Fourier Feature PINN (NF-FF-PINN) framework that embeds structural natural frequencies into the Fourier feature mapping, theoretically aligning the neural representation spectrum with the physical frequency content of the structure. This eliminates manual parameter tuning and enhances multi-frequency response accuracy. Extensive numerical validations demonstrate that NF-FF-PINNs achieve the relative displacement L<sub>2</sub> error below 2%, significantly lower than those of conventional PINNs and FF-PINNs, and stably converge within 5 × 10<sup>3</sup> iterations. Time- and frequency-domain analyses confirm the method’s information reconstruction capability, showing accurate recovery of both low- and high-frequency components with minimal loss. Moreover, noise analysis demonstrates that, compared with the traditional Newmark method, the proposed approach exhibits superior robustness and stability under data perturbations. By introducing natural frequencies as Fourier feature hyperparameters, this study broadens the applicability of physics- informed machine learning and provides a robust framework for structural analysis under earthquake excitation.</p>

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Structural natural frequency-embedded Fourier feature physics-informed neural networks for earthquake dynamic response prediction

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Xiaxing Wang,
  • Ke Du,
  • Zepeng Li,
  • Huan Luo

摘要

Conventional Physics-Informed Neural Networks (PINNs) with fully connected architectures have shown potential in solving differential equations, yet their inherent spectral bias limits accurate reconstruction of high-frequency components—critical for structural dynamics under broadband earthquake excitations. To overcome this limitation, we propose a Natural Frequency-Based Fourier Feature PINN (NF-FF-PINN) framework that embeds structural natural frequencies into the Fourier feature mapping, theoretically aligning the neural representation spectrum with the physical frequency content of the structure. This eliminates manual parameter tuning and enhances multi-frequency response accuracy. Extensive numerical validations demonstrate that NF-FF-PINNs achieve the relative displacement L2 error below 2%, significantly lower than those of conventional PINNs and FF-PINNs, and stably converge within 5 × 103 iterations. Time- and frequency-domain analyses confirm the method’s information reconstruction capability, showing accurate recovery of both low- and high-frequency components with minimal loss. Moreover, noise analysis demonstrates that, compared with the traditional Newmark method, the proposed approach exhibits superior robustness and stability under data perturbations. By introducing natural frequencies as Fourier feature hyperparameters, this study broadens the applicability of physics- informed machine learning and provides a robust framework for structural analysis under earthquake excitation.