  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 learns is a 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. 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.
