RETRACTED: Model Order Reduction Method Based on Machine Learning for Parameterized Time-Dependent Partial Differential Equations (Retracted Article)

In this paper, we propose a data-driven model order reduction method to solve parameterized time-dependent partial differential equations. We describe the system with the state variable equations, and represent a class of candidate models with the artificial neural network. The discrete L-2 error between the output of artificial neural network and the high-fidelity solution is minimized with the state variable equations and initial conditions as constraints. Therefore, the model order reduction problem can be described as a kind of optimization problem with constraints, which can be solved by combining Levenberg-Marquardt algorithm and linear search algorithm, followed by sensitivity analysis of the artificial neural network parameters. Finally, by a number of calculating examples, compared to the model-based model order reduction method, data-driven model order reduction method is non-intrusive, is not limited to state variable degrees of freedom. We can find that the data-driven model order reduction method is better than the model-based model order reduction method in both computation time and precision, and has good approximation properties.