Parameterized nonintrusive reduced-order model for general unsteady flow problems using artificial neural networks

A nonintrusive reduced-order model for nonlinear parametric flow problems is developed. It is based on extracting a reduced-order basis from high-order snapshots via proper orthogonal decomposition and using multilayered feedforward artificial neural networks to approximate the reduced-order coefficients. The model is a generic and efficient approach for the reduction of time-dependent parametric systems, including those described by partial differential equations. Since it is nonintrusive, it is independent of the high-order computational method and can be used together with black-box solvers. Numerical studies are presented for steady-state isentropic nozzle flow with geometric parameterization and unsteady parameterized viscous Burgers equation. An adaptive sampling strategy is proposed to increase the quality of the neural network approximation while minimizing the required number of parameter samples and, as a direct consequence, the number of high-order snapshots and the size of the network training set. Results confirm the accuracy of the nonintrusive approach as well as the speed-up achieved compared with intrusive hyper-reduced-order approaches.