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The article explains the convolutional LSTM (ConvLSTM) network in detail andintroduces an improved auto-encoder version of the ConvLSTM network calledAE-ConvLSTM. AE-ConvLSTM is also a sequence to sequence network that canpredict long time evolution of a dynamical system by passing hidden states fromone encoder to another. The network performed well in predicting the dynamicevolution of unsteady 2-D viscous Burgers when trained using data and, inanother case, using governing equation (without data), i.e.,physics-constrained. Further, AE-ConvLSTM was used in an effort to predict thetime evolution of two unsteady Navier-Stokes problems. These problems havecoupled pressure and velocity field having different magnitude order, and thesefields evolve in time at a different rate. It was observed that the networkcould be trained using data, but while training using physics-constrained viagoverning equations, AE-ConvLSTM fails to train for time evolution.

Sequence to sequence AE-ConvLSTM network for modelling the dynamics of PDE systems