RINA - Démonstrateur d’utilisation de l’intelligence artificielle pour la gestion opérationnelle des risques naturels gravitaires géologiques | FEREC 2020

Appendix B Bibliography about point process related to Deep Neural Network Only recent works (since 2016) investigated DNN for point process. Several sub-family are used in such task, mainly Recurrent Neural Network (RNN) with an hidden layer that endorse memory through time (papers [5] [8] [9] [11] ), NARX model [1] , Spiking Neural Network (convolutional network ??) and . Hereafter, we enumerate and sum up some related papers with citation of meaning-full part. Paper Boussaada 2018 [1] NARX models "Actually, NARX concept is a nonlinear generalization of the Autoregressive Exogenous (ARX), which is a standard instrument in linear black-box system identification. There are two different architectures of NARX neural network model, series-parallel architecture (named also open-loop) and parallel architectures (named also close-loop) given by equations below (see Figure B.1 for illutration)" ˆ y ( t + 1) = F [ y ( t ) , y ( t − 1) , ...y ( t − n y ) , x ( t + 1) , x ( t ) , ...x ( t − n x )] (B.1) ˆ y ( t + 1) = F [ˆ y ( t ) , ˆ y ( t − 1) , ... ˆ y ( t − n y ) , x ( t + 1) , x ( t ) , ...x ( t − n x )] (B.2) where F ( . ) is the mapping function of the neural network, ˆ y ( t + 1) is the predicted output of the NARX for the time t + 1 . ˆ y ( t ) , ..., ˆ y ( t − n y ) are past outputs of the NARX. y ( t ) ,..., y ( t − n y ) are the true past values of the times series. x ( t + 1) , ..., x ( t − n x ) are the inputs of the NARX. n x and n y are numbers of input/output delays. Paper N. Du 2016 [5] Du et al. [5] proposed to use an RNN to model the conditional intensity function. In this approach, an input vector x i , which extracts the information of the event time t i , is first fed into 45