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Incremental Dynamic Analysis (IDA) is a powerful method for the seismic performance assessment of structures. IDA is also very efficient for handling epistemic uncertainty, i.e. uncertainty due to the mechanical properties of the structure. In the latter case, IDA should be performed within a Monte Carlo framework requiring the execution of a vast number of nonlinear response history analyses. The increased computing effort renders the calculation of performance statistics time-consuming and hence the method is not always practical. We propose a scheme based on artificial neural networks (NN) in order to reduce the computational effort and allow using the method on many applications. Within a Monte Carlo framework, trained Neural Networks can rapidly generate a large sample of IDA curves which are then post-processed to calculate useful response statistics. The implementation of the proposed method is quick, straightforward and gives accurate seismic performance estimations.