FNO-PD: A Fourier neural operator-based physics-based data-driven framework for efficient dynamic response computation in vehicle-track coupled systems

Accurate and efficient computation of dynamic responses in vehicle-track coupled systems is essential for safe, smooth, and reliable high-speed railway operation and maintenance optimization. However, traditional numerical simulation methods exhibit a significant efficiency bottleneck in solving large-scale dynamic problems, while existing deep learning approaches struggle to accurately characterize the global dynamic coupling characteristics of the system. To address these challenges, this study proposes a novel Fourier neural operator-based physics-based data-driven (FNO-PD) framework for the efficient prediction of dynamic responses in vehicle-track coupled systems. The framework comprises a physics-driven module and a data-driven module: the physics-driven module integrates physical information into FNO to predict train dynamic responses, while the data-driven module combines proper orthogonal decomposition (POD) with FNO for rail displacement field prediction. The accuracy and efficiency of the proposed framework are evaluated using the probability density evolution method (PDEM) as a benchmark. Within the same vehicle-track numerical framework, the model is assessed for numerical generalization under measured track irregularity inputs, near-range speed extrapolation, and robustness to noise interference. Results demonstrate that the FNO-PD framework achieves high prediction accuracy and online computational efficiency, with good agreement between its predictions and the PDEM results. During online prediction, the proposed method achieves an approximately 1200-fold speedup over PDEM. Tests conducted with measured track irregularity inputs at speeds within and just outside the training range, together with noise interference tests, indicate satisfactory numerical generalization and noise robustness under the tested conditions. This study provides a novel and efficient technical pathway for the numerical prediction of dynamic responses in vehicle-track coupled systems, with potential for large-scale numerical analyses in high-speed railway engineering.