EAAI Journal 2026 Journal Article
A label-free physics informed neural network with hard constraints and Fourier features spectrally-enhanced for multi-frequency seismic structural dynamic response
- Ke Du
- Zehua Huang
- Jiaxin Li
- Dongwang Tao
- Zhuoshi Chen
The seismic response of civil structures typically exhibits broadband and high-frequency components, posing significant challenges for traditional Physics-Informed Neural Networks (PINN). Traditional PINN suffer from inherent spectral bias, which limits their ability to capture high-frequency dynamics, and gradient pathology arising from the treatment of initial conditions as soft constraints, which often leads to unstable convergence and reliance on labeled data. To overcome these limitations, this paper proposes a novel label-free, spectrally-enhanced framework: the PINN with Hard Constraints and Fourier Features (HCFF-PINN). The proposed method integrates a physics-guided Fourier feature mapping layer into the input space, substantially enriching the network's spectral representation and alleviating the intrinsic low-frequency preference of standard fully connected architectures. In addition, initial conditions are rigorously enforced via hard constraints embedded directly into the network structure, eliminating the need for labeled data and avoiding gradient imbalance caused by multi-term loss functions. The HCFF-PINN framework is applied to solve the dynamic equilibrium equations of structural systems under earthquake excitation. Numerical experiments on single- and multi-degree-of-freedom systems subjected to diverse earthquake excitations demonstrate the superiority of the proposed framework. Results indicate that HCFF-PINN achieves significantly higher accuracy and training efficiency compared to traditional PINN and advanced PINN variants, particularly in reconstructing high-frequency response components. This work establishes HCFF-PINN as a robust, efficient, and fully physics-driven tool for complex structural responses analysis under earthquake excitation. (The replication code for this study is publicly available on GitHub: https: //github. com/duke-iem/AIStructDynSolve.)