Latent Neural PDE Solver: a reduced-order modelling framework for
  partial differential equations
Zijie Li Saurabh Patil Francis Ogoke Dule Shu Wilson Zhen Michael Schneier John R. Buchanan, Jr. Amir Barati Farimani
Neural networks have shown promising potential in accelerating the numerical
simulation of systems governed by partial differential equations (PDEs).
Different from many existing neural network surrogates operating on
high-dimensional discretized fields, we propose to learn the dynamics of the
system in the latent space with much coarser discretizations. In our proposed
framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first
trained to project the full-order representation of the system onto the
mesh-reduced space, then a temporal model is trained to predict the future
state in this mesh-reduced space. This reduction process simplifies the
training of the temporal model by greatly reducing the computational cost
accompanying a fine discretization. We study the capability of the proposed
framework and several other popular neural PDE solvers on various types of
systems including single-phase and multi-phase flows along with varying system
parameters. We showcase that it has competitive accuracy and efficiency
compared to the neural PDE solver that operates on full-order space.