Preserving kinematic synchronization in fluid–structure interactions via high-order spatiotemporal neural surrogate models

Fully coupled fluid–structure interactions (FSI), notably vortex-induced vibrations, present severe computational bottlenecks for real-time forecasting and active flow control. Existing data-driven surrogates often exhibit error accumulation and phase drift in long-horizon FSI prediction, especially under strong non-linear coupling. To address these modeling gaps, we introduce a physics-informed multi-scale spatiotemporal transformer (PI-MST) that combines multi-resolution representation learning with discrete physics regularization. Rather than relying on standard auto-differentiation, the model uses fourth-order central differences for spatial gradients and a second-order backward differentiation formula scheme for temporal residual construction during training. Furthermore, a macroscopic turbulent kinetic energy (k) channel is included as an auxiliary physics state to improve closure-related consistency in high-Reynolds-number cases. To improve training stability under the stiff partial differential equation constraints associated with coupled boundaries, a bounded curriculum strategy is used to balance data and physics losses and reduce optimization instability in early training. Under aligned 10-in/6-out and block-wise autoregressive rollout evaluation across broad Reynolds variants (Re ∈ [50, 1 × 106]), PI-MST reduces field and kinematic errors vs unconstrained baselines. Under autonomous rollout, it delays error growth and preserves phase-consistent force-displacement behavior over a finite horizon. These results indicate that explicit discrete physics regularization can improve the practical robustness of FSI surrogates within the tested regimes and prediction horizons.