The field of equivariant neural networks and deformable object simulation is rapidly advancing, with a focus on improving the accuracy and efficiency of simulations. Recent developments have introduced new architectures and methods that incorporate symmetries and equivariances, enabling more realistic and scalable simulations. Notably, researchers have proposed novel equivariant neural networks that can handle complex tasks such as deformable object simulation, soft tissue deformation, and molecular generation. These models have achieved state-of-the-art performance on various benchmarks, demonstrating their potential for real-world applications. Furthermore, the use of data-driven approaches and hierarchical graph neural networks has improved the accuracy and efficiency of simulations, allowing for more complex and realistic scenarios to be modeled.

Some noteworthy papers in this area include EqCollide, which introduces an equivariant neural fields simulator for deformable objects and their collisions, and Diffusion-Based Hierarchical Graph Neural Networks, which proposes a novel learned simulator that integrates rolling diffusion and hierarchical graph neural networks to capture global phenomena and long-range correlations. Additionally, Neural-Augmented Kelvinlet presents a novel physics-informed neural simulator for soft tissue deformation, and EquiCaps introduces a predictor-free pose-aware pre-trained capsule network for equivariant learning.