A causality-DeepONet for causal responses of linear dynamical systems (Q6584819)

Computing operators between physical quantities defined in function spaces have many applications in scientific and engineering computations and in forward and inverse problems. In the paper under review, the authors study the DeepONet for time-dependent operators from physical systems such as those encountered in studying seismic wave response problems. The authors propose Causality-DeepONet to ensure the causality of the retarded Green's function of the underlying differential equation between the input seismic ground accelerations and the output building responses. The authors also use the time homogeneity of a dynamic system in the design of the neural network by encoding the convolutional nature of the retarded Green's function in the choice of the network weights. The proposed DeepONet with built-in causality allows the authors to learn, accurately and with minimum requirement of training data, the mapping between the ground accelerations and the corresponding displacements of the building at the roof level excited by the seismic ground accelerations.\N\NThe paper is well written with a good set of references.