POD—ANN Reduced Order Macromodel of Nonlinear Autonomous Dissipative System Using Machine Learning

Abstract

AbstractReal-world problems are addressed effectively and safely using simulation modeling. Simulation modeling gives highly appreciable solutions by providing a clear picture of complex systems. The reason for the same is that nonlinear structure of real-world problems with complexities cannot be handled by linearized models. Further, computational complexities of large-scale dynamical system simulations occurring in such situations will be reduced by model order reduction (MOR). This is further improved with the use of artificial neural networks (ANNs). In this paper, the generalized neural network modeling of nonlinear autonomous dissipative system using machine learning and proper orthogonal decomposition (POD) has been addressed, which is a novel one. The fluid mechanical model considered here is trained with multiple temporal swatches evolved on different parametric variations and trialed out at different time instances. Machine learning tries to learn such models by analyzing snapshot observations from active systems. The neural network developed by machine learning is able to make better prediction for validating data which is different from the training data set. The complexity of the data set generated by nonlinear autonomous dissipative system is reduced by applying the POD on the original data set. This demonstrates that the neural network is successfully utilized to macromodel the autonomous dynamical system.KeywordsMachine learningNeural networkAutonomous systemDissipative systemsBurgers’ equationFinite difference method