## 1 Introduction
[12] predicted the nonlinear inter-story drifts of three building structures (five degrees-of-freedom system, six-story instrumented RC building, and three-story steel building model) using the Long Short-Term Memory [13] (LSTM) recurrent networks. In general, very high prediction accuracy was observed for a close-to-linear structural response, and it decreases with nonlinearities. The same research team had improved the prediction accuracy and robustness of the previously developed LSTM models by encoding some laws of physics in the network architecture and embedding them in the overall loss function [14]. [PERSON] et al. [10] developed a physics-based recurrent cell (DynNet) that predicts the full state space (acceleration, velocity, displacement, and internal force) of multi degrees of freedom (MDOF), given a ground motion. Nonlinear responses of two four-degree of freedom systems with different nonlinearity types (elastoplastic and nonlinear elastic stiffnesses) were quite successfully predicted; thus, concluding that the performance of the DynNet in capturing the nonlinear response is promising. All these implementations of RNNs for RPPs highlighted some drop of accuracy in predicting large nonlinearities, and their respective models remain limited to predict limited response quantities of the studied structures. In order to address many of the aforementioned limitations, the current study combines the advantages of both NTHA (mechanics-based method) and MLMs (data-driven method) to propose a hybrid seismic analysis for building structures. The term hybrid is related to the time integration algorithm of the NTHA, not to the input data nor to the model architecture. Some existing or newly developed materials, structural components, or devices may have an excessively complicated analytical model and/or a still not-exhaustive understanding of their true behavior among researchers and practitioner communities. Instead of adopting simplified analytical models based on many assumptions which introduce a modeling error, an RNN trained by available experimental data can capture the true behavior of the target component or group of components, then be used to make predictions on new unseen data at each time-step of the hybrid seismic analysis proposedin this study. Therefore, this paper presents the novelty of implementing DL models into the numerical time-integration algorithm, targeting only structural components of interest. The resulting hybrid seismic analysis is not limited to a specific building structure since the MLM can be saved and reused in any new building model containing the same target components, it can compute the full dynamic response, and it aims to increase further the accuracy of conventional NTHAs. Since this paper represents the first attempt at such an application of DL in earthquake engineering, artificial data are generated and used in this study to check the validity of the method. After a presentation of the principle of the proposed hybrid seismic analysis, the properties of the three isolated-building models and the four ground motions used in this study are described. Then, a comprehensive framework for generating synthetic data, designing, and testing RNN models is proposed and applied to develop three MLMs simulating the isolation layer of respective buildings. Eventually, these MLMs are implemented to perform twelve hybrid analyses whose results are compared with those of conventional NTHAs. The efficiency of the proposed hybrid analysis is checked in terms of accuracy and necessary computation time. Further related studies are proposed in the conclusion section.