  We address the problem of accelerating thin-shell deformable object
simulations by dimension reduction. We present a new algorithm to embed a
high-dimensional configuration space of deformable objects in a low-dimensional
feature space, where the configurations of objects and feature points have
approximate one-to-one mapping. Our key technique is a graph-based
convolutional neural network (CNN) defined on meshes with arbitrary topologies
and a new mesh embedding approach based on physics-inspired loss term. We have
applied our approach to accelerate high-resolution thin shell simulations
corresponding to cloth-like materials, where the configuration space has tens
of thousands of degrees of freedom. We show that our physics-inspired embedding
approach leads to higher accuracy compared with prior mesh embedding methods.
Finally, we show that the temporal evolution of the mesh in the feature space
can also be learned using a recurrent neural network (RNN) leading to fully
learnable physics simulators. After training our learned simulator runs
$500-10000\times$ faster and the accuracy is high enough for robot manipulation
tasks.
