Accurate prediction of nonlinear structural responses is essential for earthquake risk assessment and management. While high-fidelity nonlinear time history analysis provides the most comprehensive and accurate representation of the responses, it becomes computationally prohibitive for complex structural system models and repeated simulations under varying ground motions. To address this challenge, we propose a composite learning framework that integrates simplified physics-based models with a Fourier neural operator to enable efficient and accurate trajectory-level seismic response prediction. In the proposed architecture, a simplified physics-based model, obtained from techniques such as linearization, modal reduction, or solver relaxation, serves as a preprocessing operator to generate structural response trajectories that capture coarse dynamic characteristics. A neural operator is then trained to correct the discrepancy between these initial approximations and the true nonlinear responses, allowing the composite model to capture hysteretic and path-dependent behaviors. Additionally, a linear regression-based postprocessing scheme is introduced to further refine predictions and quantify associated uncertainty with negligible additional computational effort. The proposed approach is validated on three representative structural systems subjected to synthetic or recorded ground motions. Results show that the proposed approach consistently improves prediction accuracy over baseline models, particularly in data-scarce regimes. These findings demonstrate the potential of physics-guided operator learning for reliable and data-efficient modeling of nonlinear structural seismic responses.

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