The paper presents a combined methodology for the operational forecasting of maximum wave height, integrating the strengths of spectral wave models, phase-resolving simulations, and machine learning to address the core limitations inherent in each approach. The procedure begins with a frequency-directional wave spectrum obtained from the WAVEWATCH III model, which is subsequently transformed into a wavenumber field and used as initial conditions for the phase-resolving model TRIDWAVE. This step enables the generation of a realistic nonlinear wave field from which the target extreme parameter (maximum wave height) is extracted. To circumvent the prohibitive computational cost associated with repeatedly executing the phase-resolving model, a feedforward neural network was developed and trained to act as a fast surrogate, learning the mapping from input wave spectra to the corresponding maximum height values as calculated by TRIDWAVE. Validation experiments conducted for the Baltic Sea demonstrate that the trained network predicts maximum wave height with an average relative error of approximately 5 %. This result confirms the network’s capability to accurately infer key nonlinear statistics directly from linear spectral input.