A multi-scale framework to predict hydrodynamic loads of a ventilated cavitating body

An axisymmetric body enveloped by the shedding ventilated cavity is subject to significant pulsations in hydrodynamic loads, which can compromise its motion stability. To mitigate instability, engineering practice typically employs real-time control systems that monitor hydrodynamic loads and adjust the cavity shape through ventilation and rudder deflection. However, hysteresis effects often degrade control performance. To address this challenge, this paper proposes a multi-scale prediction framework integrating Transolver-enhanced Kolmogorov–Arnold Network (TransKAN) and Gaussian Process Regression (GPR) to achieve long-term forecasting of lateral force and torque. The lateral force and torque are decomposed into time-averaged and pulsating components, which are modeled by GPR and TransKAN, respectively. Under optimal hyperparameter configurations, the TransKAN model demonstrates high fidelity and efficiency in predicting pulsating components, and ablation studies confirm the performance gain introduced by the Kolmogorov–Arnold Network (KAN) to the base Transolver architecture. Finally, the integrated multi-scale predictions yield mean relative errors of 3.31% and 3.70% for total lateral force and torque, with an amplitude spectrum cosine similarity of 0.9997 relative to ground truth, indicating strong agreement in both time and frequency domains. By enabling anticipatory compensation for hysteresis-induced delays, this proposed method significantly enhances the robustness of control systems and exhibits strong potential for practical engineering applications.