In recent years, the global demand for renewable energy has increased due to worldwide efforts to mitigate climate change and realize a sustainable society. Among various renewable energy sources, offshore wind power has attracted significant attention owing to its higher and more stable wind conditions compared to onshore systems, enabling improved power generation efficiency. In particular, floating offshore wind turbines offer substantial advantages in deep-water regions, although their design requires careful evaluation of fatigue resistance and structural integrity under complex, coupled wind–wave loading conditions. For such large-scale and highly nonlinear dynamical systems, high-fidelity numerical simulations based on computational mechanics are indispensable for accurately evaluating structural responses. However, these simulations are computationally expensive, making parametric studies, optimization, and uncertainty quantification prohibitively costly. To overcome this limitation, surrogate modeling based on machine learning has emerged as a promising alternative. Nevertheless, conventional data-driven models, such as convolutional neural networks (CNNs), are fundamentally limited by their reliance on local convolution operators and fixed-resolution representations, which restrict their ability to generalize across varying temporal scales, loading conditions, and discretizations. In this study, neural-operator-based surrogate models are developed to predict the time-series blade displacement of floating offshore wind turbines using wind and wave analysis data. As a baseline, a CNN-based neural operator is constructed to model the temporal evolution of blade deformation. To overcome the intrinsic limitations of local convolution and to achieve mesh-independent and resolution-agnostic learning of the underlying input–output mapping, a Fourier Neural Operator (FNO) is introduced. The FNO learns the solution operator in the spectral domain, enabling efficient representation of global, nonlocal interactions inherent in structural dynamics governed by partial differential equations. A systematic comparison between CNN-based and FNO-based surrogate models is conducted in terms of prediction accuracy, robustness, and generalization performance under unseen wind and wave conditions. The performance of the FNO-based model is explicitly compared with that of the CNN-based model. The necessity of operator learning frameworks, such as FNO, for surrogate mode