An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator
This addresses the problem of solving PDEs for computational physics and engineering, offering a novel architecture that enhances predictive performance, though it appears incremental as it builds on existing neural network and physics-informed methods.
The study tackled solving partial differential equations (PDEs) by proposing an unsupervised convolutional neural network with nonlocal interactions, using a peridynamic differential operator as a filter and a modified ConvLSTM for periodic physics, and demonstrated improved extrapolation capability compared to PINN-type solvers.
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.