  The goal of this work is to address two limitations in autoencoder-based
models: latent space interpretability and compatibility with unstructured
meshes. This is accomplished here with the development of a novel graph neural
network (GNN) autoencoding architecture with demonstrations on complex fluid
flow applications. To address the first goal of interpretability, the GNN
autoencoder achieves reduction in the number nodes in the encoding stage
through an adaptive graph reduction procedure. This reduction procedure
essentially amounts to flowfield-conditioned node sampling and sensor
identification, and produces interpretable latent graph representations
tailored to the flowfield reconstruction task in the form of so-called masked
fields. These masked fields allow the user to (a) visualize where in physical
space a given latent graph is active, and (b) interpret the time-evolution of
the latent graph connectivity in accordance with the time-evolution of unsteady
flow features (e.g. recirculation zones, shear layers) in the domain. To
address the goal of unstructured mesh compatibility, the autoencoding
architecture utilizes a series of multi-scale message passing (MMP) layers,
each of which models information exchange among node neighborhoods at various
lengthscales. The MMP layer, which augments standard single-scale message
passing with learnable coarsening operations, allows the decoder to more
efficiently reconstruct the flowfield from the identified regions in the masked
fields. Analysis of latent graphs produced by the autoencoder for various model
settings are conducted using using unstructured snapshot data sourced from
large-eddy simulations in a backward-facing step (BFS) flow configuration with
an OpenFOAM-based flow solver at high Reynolds numbers.
