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 10−100× faster and the accuracy is high enough for robot manipulation tasks.