Tool wear is one of main factors to evaluating the performance of a machining process. To improve the lifespan of cutting tools, coated tools have become indispensable in modern machines for higher productivity. Nevertheless, predicting the wear progression of coated tools by analytical (white-box) models is extremely challenging and time-consuming as the cutting process involves complex, multi-layered, and process-dependent interactions. To ensure the machining quality and sustainability, manufacturers apply digital twins to not only detect errors but also to predict the lifespan of the tool coatings. Data-driven machine learning models can achieve high prediction accuracy with available sufficient sensing data [2]. However, these black-box models generally lack interpretability and adaptability across different cutting conditions. To enable computationally efficient prediction of dynamic wear, it is essential to incorporate prior physical knowledge into data-driven models such as grey-box models. Techniques such as physical-informed neural network (PINN) and Gaussian processes (GPs) have gained increasing attention [3,4]. PINNs embed governing physical laws directly into the training process through additional terms in the loss function, enabling the learning of physically consistent representations. However, they often require careful tuning of loss terms and substantial computational effort. In contrast, physics-guided GPs incorporate physical knowledge through structured covariance functions or prior mean models, resulting in probabilistic models with fewer parameters and inherent uncertainty quantification. In this talk we discuss the construction of grey-box models based on physics-informed GPs for wear prediction of coated tools in turning processes, and investigate the influence of process parameters and multiple sensor data including forces, acceleration, and temperatures [1]. Further, we analyze how GPs allow to quantify uncertainties, and thus enable designing experiments in a targeted manner.