Prediction of spatiotemporal dynamics using deep learning: Coupled neural networks of long short-terms memory, auto-encoder and physics-informed neural networks

Several classic reaction-diffusion models using partial differential equations (PDEs) have been established to elucidate the formation mechanism of vegetation patterns. However, predictive modeling of complex spatiotemporal dynamics using traditional numerical methods can be significantly challenging in many practical scenarios. Physics-Informed Neural Networks (PINNs) provide a new approach to predict the solution of PDEs. However, the generalization of PINNs is not satisfactory when pretrained PINNs is directly used in non-trained space (defined as explorations). This may be attributed to the lack of training in the time dimension. Therefore, a framework (LA-PINNs) is proposed to predict the evolutionary solution of the non-dimensional vegetation-sand model. The framework couples neural networks of Long-Short Terms Memory, Auto-Encoder and Physics-Informed Neural Networks. The predictions of LA-PINNs are much better than those of PINNs. Then we studied the effects of hyperparameters on the accuracy of predictions. Based on training in time dimension by LSTM module and pretraining for quick-training strategy, LA-PINNs can improve the accuracy of explorations.