Baseline-informed Fourier neural operator correction for nonlinear wave loads on monopile foundations under steep regular waves

Reliable prediction of horizontal wave loads remains important for preliminary assessment of offshore monopile foundations under steep regular waves. The Rainey semi-analytical model efficiently predicts the dominant periodic load but does not fully capture local waveform features associated with secondary load cycles. This study uses computational fluid dynamics (CFD) simulations as the numerical reference and defines the difference from the Rainey solution as a correction target over one wave period. A Fourier neural operator (FNO) learns this correction from dimensionless wave and geometry parameters and the complete Rainey force history; adding the predicted correction to the Rainey baseline yields the Theory+FNO total force. On 20 independent test cases, Theory+FNO and Rainey give mean total-force normalized root mean square errors of 2.56% and 9.08%, respectively, against the CFD reference. The correction improves the representation of local secondary load-cycle features and gives lower errors than direct total-force FNO prediction in the complete diameter holdouts. The framework provides rapid horizontal-load estimates for circular monopiles within the investigated range of steep regular waves.