Fast Dynamics Solution Method for Pantograph-Catenary System Based on Diffusion-Enhanced Fourier Operator

The dynamic characteristics of the pantograph-catenary system (PCS) directly affect the current collection quality and operational safety of high-speed trains. While traditional finite element methods (FEM) that utilize nonlinear cable-truss equivalent models accurately characterize the strong nonlinearity and time-varying mechanical behaviors of the PCS, they suffer from prohibitive computational complexity that hinders real-time prediction and digital twin deployment. To address these computational bottlenecks, data-driven surrogate models have emerged. However, standard Fourier neural operators (FNO) rely on fixed-frequency band truncation, which effectively captures low-frequency principal modes but systematically discards critical high-frequency transient details, such as localized contact force mutations and wave reflections. Purely data-driven models also lack explicit physical constraints, leading to severe error accumulation during long-term dynamic simulations. To overcome these multiscale modeling challenges, this paper proposes adaptive fourier neural operator diffusion model (AFNODM), a novel physics-informed framework that synergistically integrates an adaptive fourier neural operator (AFNO) with a conditional diffusion model (CDM) to establish a time-frequency collaborative generation paradigm. In the first stage, the AFNO acts as a global physical skeleton generator to capture dominant vibration modes (0–20 Hz). Crucially, we introduce a velocity-based frequency modulation mechanism equipped with deformable convolution kernels, allowing the model to adaptively adjust its spectral receptive field in response to real-time train speeds and neutralize Doppler effects. In the second stage, a CDM-driven post-processing architecture is deployed. Conditioned on the AFNO’s output, the diffusion model executes a progressive reverse denoising strategy in the latent space to seamlessly reconstruct the missing high-frequency residual details (above 20 Hz), while kinematic constraint losses are embedded via automatic differentiation to ensure absolute derivative consistency across spatial-temporal fields. Extensive evaluations on a high-fidelity PCS dataset (200–380 km·h^–1) demonstrate that AFNODM efficiently solves complex dynamic equations with an unprecedented balance of speed and precision. At 350 km·h^–1, the root mean square errors (RMSE) for the displacement, velocity, and acceleration fields are remarkably low at 0.0673, 0.1603, and 0.8503, respectively, representing an error reduction of over 50% compared with mainstream baselines such as deep operator network (DeepONet) and physics-informed enhanced fourier neural operator (PI-EFNO). Frequency-domain analysis confirmed that CDM integration significantly suppressed the high-frequency relative spectral error (RSE) from 16.80% (using pure AFNO) to 6.55%. Cross-line robustness tests across three distinct high-speed railway configurations (Beijing—Shanghai, Guangzhou—Shenzhen, and Beijing—Tianjin) validated the exceptional generalization capabilities of the model under varying structural parameter perturbations. Ultimately, the proposed AFNODM framework provides a highly accurate, resolution-independent, and real-time capable computational engine, paving the way for next-generation digital twins and intelligent predictive maintenance in modern electrified railways.