## 6 Conclusions  
A hybrid seismic analysis is elaborated in this paper to compute the full response of a building structure by incorporating both analytical and RNN models into an explicit time integration method. The MLM would predict the nonlinear response of interest at each time step of the computation. A comprehensive framework is proposed for generating artificial data, optimizing the network architecture and hyperparameters, training the MLM, and eventually testing it. Numerical simulations of three isolated buildings (5, 10, and 15 stories) subjected to four GMs of different amplitudes, frequency contents, and durations are performed to check the efficiency of the proposed hybrid analysis. The developed MLMs simulate the isolation layer (NRB + LRB + Oil Damper) of studied buildings by mapping its displacement time history to the corresponding shear force-time history. They were tested then implemented to perform a total of twelve hybrid seismic analyses. Hence, the following conclusions are formulated:  
1. The proposed hybrid seismic analysis computes the full response in terms of acceleration, velocity, and displacement at each degree of freedom. The term hybrid is related to the time integration algorithm, not to the input data nor to the MLM architecture, offering a novel application of ML in civil engineering. Once the MLM is developed, it can be saved and reused to perform structural analysis of any building model containing the same component or group of components the MLM was trained to simulate. Therefore, the novel hybrid analysis proposed in this paper overcomes the shortcoming of most applications of ML in structural RPPs being limited to predicting specific response quantity(s) of the structure(s) used in the training process. 2. The framework proposed for developing the MLMs considers the main three steps to design a sequence-to-sequence prediction model: data framing, tuning of model architecture, and diagnosis of learning behavior. A shallow GRU model with two recurrent layers of 60 cells each and a one-unit Dense layer as an output layer has been found the most appropriate in terms of accuracy, reliability (similar performance after 150 repetitions), and simplicity (only 33,361 trainable parameters). The MSEs on scaled training and validation data decreased below 5 \(\times\) 10\({}^{-5}\) after only 1000 epochs and were in the order of 10\({}^{-4}\) on testing data. The optimized RNN architecture may be used for similar structural RPPs, and the proposed framework is highly recommended to design RNN models for different sequence-to-sequence prediction problems. 3. The hybrid seismic analyses responses of the studied building models under the four GMs are compared with results of the conventional analysis (OpS method) taken as a reference in this study. The linear response of the superstructures is very well evaluated with a maximum drift RMSE (respectively shear RMSE) of 0.00528 cm (respectively 27.1 kN) among all the twelve cases. The hybrid analysis could accurately capture the nonlinear hysteresis loops of isolation layers. The maximum drift RMSE (respectively shear RMSE) at the isolation level was 0.338 cm (respectively 46.3 kN) among all configurations. These results offer a numerical validation of the accuracy of the proposed hybrid seismic analysis since all RMSEs are considered acceptable in the earthquake engineering practice. 4. The necessary computation times for developing the MLMs and performing the hybrid seismic analyses were provided to check the applicability of such a study by practitioners. Optimizing the RNN architecture is the most time-consuming stage in the whole framework. A total duration of 67.42 h, counting 630 independent training acts, was necessary to find out an accurate and reliable simple architecture capable of simulating the structural behavior of both deformation- and velocity-dependent devices simultaneously. The hybrid seismic analysis is far less time-consuming, and it takes an average of 0.27 s per integration time-step for a standard CPU.