Tsunami models have been developed for several decades, and many have shown good agreement with observations from real world events. The model solves wave equations, but simulation is usually computationally expensive in a large-scale basin. To assess potential tsunami impacts, ensemble analysis is standard for sampling source uncertainties, but computational costs constrain the number of scenarios that can be evaluated. Machine‑learning approaches have been developed to reduce the computational burden and accelerate typical tsunami‑ensemble analyses. However, these surrogate models are usually task-specific; they emulate buoy signals, sensor inputs, and maximum water level maps. Recent advances in machine learning techniques, such as neural operators, allow learning full wave evolution from physics-based simulations. Here, we introduce a data-driven tsunami surrogate model based on a Factorized Fourier Neural Operator (F-FNO). Memory-efficient F-FNO supports higher Fourier mode capacity, enabling the tsunami surrogate model to learn scenario-based COMCOT simulations and generalize to unseen epicenter locations/extrapolated magnitudes. We designed logic tree-based COMCOT simulations for the East Sea (Sea of Japan) to construct a surrogate operator. The F-FNO learns tsunami propagation through a short sequence of wavefield states and creates a general operator function that generates future wave and velocity fields. From the logic tree, we hold out the largest magnitude (8.0) and one specific source location for model evaluation and to test the scalability of the neural operator. As a result, the surrogate predicted tsunami waves with root mean square errors in surface elevation of 2–8 cm and first-arrival timing errors of approximately 8–12 min. Running the F-FNO surrogate requires approximately 8.5–12 s per scenario on a single GPU, compared to 87.9–95.7 s of COMCOT simulation time. The computational efficiency of the operator and its potential to scale to larger scenario ensembles support more timely tsunami scenario analysis and can complement physics-based solvers in offshore applications.