Reduced‐order modeling framework using two‐level neural networks

Abstract

AbstractEstablished reduced‐order modeling (ROM) methods, for instance, Galerkin‐projection, approximate the solution by linearly projecting high‐dimensional spaces to a lower‐dimensional space spanned by the reduced basis. However, the accuracy of these methods may be insufficient for complex and multiscale simulations due to the restriction to a linear space. Alternatively, autoencoders (AEs) can be used for nonlinear dimensionality reduction. We combine nonlinear dimensionality reduction techniques with time series prediction to build data‐driven ROMs. The presented framework consists of two‐level neural networks. The high‐dimensional space is nonlinearly compressed in the first level using the encoder function of the AE. Subsequently, the temporal evolution of the latent vector is predicted in the second level. The original solution can be easily reconstructed using the decoder function of the AE. In comparison with the projection‐based ROMs, for example, proper orthogonal decomposition (POD) with Galerkin projection, this framework allows naturally to include parameters in the prediction without nonlinear interpolation of the linear basis. We demonstrate the framework on a two‐dimensional flow field simulation around circular bodies parameterized with the inlet fluid velocity.