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The manuscript discusses advancements in Full Waveform Inversion (FWI) for seismic imaging, focusing on reducing computational burdens through machine learning (ML). It introduces an m-step autoregressive neural operator framework for efficient simulation of forward and adjoint wavefields in 2D acoustic media. The study compares single-step and autoregressive approaches, highlighting the latter’s superior accuracy and temporal consistency. Using Fourier Neural Operators (FNO) and U-shaped FNO (UFNO), the research demonstrates significant reductions in computational time and improved performance across SEAM-type velocity models. Benchmarking results show that while UFNO achieves lower training loss, FNO offers better throughput and GPU memory efficiency, making it the preferred model for geophysical applications.