Assessment of DeepONet for time dependent reliability analysis of dynamical systems subjected to stochastic loading

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of recently proposed DeepONet in solving time dependent reliability analysis and uncertainty quantification of systems subjected to stochastic loading. Unlike conventional machine learning and deep learning algorithms, DeepONet is an operator network and learns a function to function mapping and hence, is ideally suited to propagate the uncertainty from the stochastic forcing function to the output responses. We use DeepONet to build a surrogate model for the dynamical system under consideration. Multiple case studies, involving both toy and benchmark problems, have been conducted to examine the efficacy of DeepONet in time dependent reliability analysis and uncertainty quantification of linear and nonlinear dynamical systems. Comparisons have also been drawn with Recurrent Neural Network results and with results obtained from Proper Orthogonal Decomposition based Gaussian process. The results obtained indicate that the DeepONet architecture is accurate as well as efficient. Moreover, DeepONet posses zero shot learning capabilities and hence, a trained model easily generalizes to unseen and new environment with no further training. • We investigate DeepONet for time-dependent reliability analysis. • DeepOnet learns operator and allows zero shot learning. • DeepONet accurately captures probability of failure and PDF of FPFT. • DeepONet is highly efficient and yields accurate results.