  We propose a new family of neural networks to predict the behaviors of
physical systems by learning their underpinning constraints. A neural
projection operator lies at the heart of our approach, composed of a
lightweight network with an embedded recursive architecture that interactively
enforces learned underpinning constraints and predicts the various governed
behaviors of different physical systems. Our neural projection operator is
motivated by the position-based dynamics model that has been used widely in
game and visual effects industries to unify the various fast physics
simulators. Our method can automatically and effectively uncover a broad range
of constraints from observation point data, such as length, angle, bending,
collision, boundary effects, and their arbitrary combinations, without any
connectivity priors. We provide a multi-group point representation in
conjunction with a configurable network connection mechanism to incorporate
prior inputs for processing complex physical systems. We demonstrated the
efficacy of our approach by learning a set of challenging physical systems all
in a unified and simple fashion including: rigid bodies with complex
geometries, ropes with varying length and bending, articulated soft and rigid
bodies, and multi-object collisions with complex boundaries.
