  This study presents a novel unsupervised convolutional Neural Network (NN)
architecture with nonlocal interactions for solving Partial Differential
Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is
employed as a convolutional filter for evaluating derivatives the field
variable. The NN captures the time-dynamics in smaller latent space through
encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM)
layer between them. The ConvLSTM architecture is modified by employing a novel
activation function to improve the predictive capability of the learning
architecture for physics with periodic behavior. The physics is invoked in the
form of governing equations at the output of the NN and in the latent (reduced)
space. By considering a few benchmark PDEs, we demonstrate the training
performance and extrapolation capability of this novel NN architecture by
comparing against Physics Informed Neural Networks (PINN) type solvers. It is
more capable of extrapolating the solution for future timesteps than the other
existing architectures.
