Neural network hyperreduction for parameterized computational models in nonlinear stochastic dynamics

Highly efficient hyperreduction methods have been proposed to reduce the computational cost of parameterized high-dimensional models in nonlinear dynamics. Unlike hyperreduced models, the parameterized reduced-order models still scale with the dimension of the high-dimensional model for the computation of the projected nonlinear forces. As an alternative to traditional hyperreduction methods, this work presents a neural-network-based hyperreduction strategy. It is embedded within the framework of parameterized reduced-order models in nonlinear stochastic dynamics. The proposed approach achieves hyperreduction by entirely removing such a dependence on the high-dimensional model dimension. In particular, the costly computation and projection of nonlinear forces in the high-dimensional physical space is bypassed: the neural network directly outputs the reduced forces from the reduced displacements and system parameters. It is trained on data collected during the offline stage required for constructing the parameterized reduced-order model. The resulting hyperreduced model enables substantial computational savings, particularly suited for large-scale Monte Carlo simulations in the stochastic dynamics framework. Numerical results show that the method provides highly accurate approximations of the nonlinear response and its statistics, with a performance gain of two orders of magnitude with respect to the parameterized reduced-order model.