Nonlinear dynamic mode decomposition from time-resolving snapshots based on deep convolutional autoencoder

A novel nonlinear decomposition method of flow field is proposed based on the dynamic mode decomposition (DMD) and nonlinear mode decomposition autoencoder. The flow fields are indexed in time order and then input to the nonlinear neural networks to learn the connected observables and decomposed fields. The reconstructions of input fields are assumed to be the summation of the nonlinear decomposed fields. The nonlinear decoders are regarded as the nonlinear modes, which concentrate most of the total energy of the flow field data. The resulting nonlinear dynamic mode decomposition autoencoder reports a series of orderly low-dimensional representations and decomposition fields. Besides, the proposed method can be used for dynamic modeling and returns more stable and accurate predictions with a few number of low-dimensional representations. The present method is tested with the benchmark case, flow around a circular cylinder at Reynolds number Re = 100. The results in this example indicate that the proposed method achieves higher reconstruction accuracy using fewer modes, while retaining similar temporal dynamics and mode information as proper orthogonal decomposition and DMD.