Bound-constrained nonstationary Gaussian process regression for ventilated cavitation prediction

This research is motivated by the need to predict cavity length in ventilated cavitation experiments. Given the freestream velocity and ventilation rate, the underlying physical mechanism gives rise to informative bounds and distinct shedding regimes, which in turn induce nonstationarity in the system. In this paper, we propose a novel nonstationary bounded Gaussian process regression model that simultaneously incorporates nonstationarity and bound constraints. We adopt the Gaussian process projection framework to enforce the bound constraints and propose a mixture of bounded Gaussian processes to capture nonstationarity, where each component models a locally stationary behavior consistent with the constraints. The model parameters and mixture components are estimated through a two-stage procedure. Importantly, the proposed model reveals latent physical mechanisms by identifying distinct components, thereby offering deeper scientific insights into the input-output relationship. Numerical results across test functions and the ventilated cavitation experiments validate the superiority of the proposed method. Specifically, the proposed method effectively captures the evolution of ventilated cavity structures, thereby significantly enhancing the adaptability and operational reliability of high-speed underwater vehicles under complex environmental conditions. Codes are available on https://github.com/tbai114/Nonstationary-bounded-Gaussian-process.