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The two-scale electromagnetic model is a well-established theory for simulating microwave polarimetric passive observations of a sea surface. A critical aspect is the long computational time that is required to run the forward model, which hampers the creation of large training databases or iterative simulations within retrieval algorithms. To tackle this problem, a neural network (NN) technique is proposed in this paper. In particular, we have adopted NNs to emulate a simulator named SEAWIND, which implements the two-scale model and was validated in previous works. Two training algorithms, including a regularized approach, have been considered and compared. The assessment of the proposed approach has been carried out by statistically comparing neural-network-derived simulations with SEAWIND-derived ones for two validation data sets comprising different climatic conditions, as well as by computing the azimuthal Fourier harmonic coefficients versus wind speed and atmospheric transmittance. Regressive model functions have also been used as benchmarks. This paper demonstrates the feasibility of an NN approach to efficient and effective modeling of sea-surface thermal emission and scattering.