Limitations of Fourier Neural Operators for Nonlinear Structural Response Prediction under Earthquake Excitation

Abstract

Neural operators provide a promising framework for mapping earthquake ground motions directly to structural response histories, but their accuracy for nonlinear dynamics and out-of-distribution conditions remains poorly understood. We systematically evaluate a fixed Fourier Neural Operator architecture using single- and five-degree-of-freedom systems with linear-elastic, cubic-hardening, and bilinear-hysteretic restoring forces. Our numerical tests isolate the effects of restoring-force nonlinearity, structural period, excitation frequency content, and ground-motion amplitude. Within the training regime, the mean perrecord relative L2 error increases from 0.02 for the linear system to 0.28 and 0.38 for the cubic-hardening and bilinear-hysteretic systems, respectively; corresponding five-degree-of-freedom tests confirm the deterioration for hysteretic response. Generalization degrades more severely under distribution shifts. When structural periods fall outside the 0.5–1.0s training interval, relative L2 errors exceed 1 for both single- and multi-degree-of-freedom systems. Broader excitation frequency content further reduces nonlinear prediction accuracy, even within otherwise interpolative conditions. In addition, when models trained on records with peak ground accelerations up to about 0.19 g are evaluated at amplitudes up to about 1.0 g, they underpredict the root-mean-square bilinear-hysteretic response by approximately 17%. Error decomposition further shows that residual mean offsets account for approximately 22% of the bilinear-hysteretic error, compared with 3% for the cubic-hardening system, whereas amplitude-scaling errors remain small. These results demonstrate that strong interpolation performance does not ensure accurate prediction of nonlinear structural response under changes in structural or excitation regimes.