Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability (Communications in Computational Physics, 2021)
A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarilystudied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structuresefficiently for hyperbolic conservation laws. Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers' equation with a parameterized diffusion coefficient. The two-dimensional single-mode Rayleigh-Taylor instability (RTI), where the amplitude of the small perturbationand time are considered as free parameters, is also simulated. An adaptive samplingmethod in time during the linear regime of the RTI is designed to reduce the number ofsnapshots required for POD and the training of ANN. The extensive numerical resultsshow that the ROM can achieve an acceptable accuracy with improved efficiency incomparison with the standard full order method.