  In this work, we propose a unified framework, called Visual Reasoning with
Differ-entiable Physics (VRDP), that can jointly learn visual concepts and
infer physics models of objects and their interactions from videos and
language. This is achieved by seamlessly integrating three components: a visual
perception module, a concept learner, and a differentiable physics engine. The
visual perception module parses each video frame into object-centric
trajectories and represents them as latent scene representations. The concept
learner grounds visual concepts (e.g., color, shape, and material) from these
object-centric representations based on the language, thus providing prior
knowledge for the physics engine. The differentiable physics model, implemented
as an impulse-based differentiable rigid-body simulator, performs
differentiable physical simulation based on the grounded concepts to infer
physical properties, such as mass, restitution, and velocity, by fitting the
simulated trajectories into the video observations. Consequently, these learned
concepts and physical models can explain what we have seen and imagine what is
about to happen in future and counterfactual scenarios. Integrating
differentiable physics into the dynamic reasoning framework offers several
appealing benefits. More accurate dynamics prediction in learned physics models
enables state-of-the-art performance on both synthetic and real-world
benchmarks while still maintaining high transparency and interpretability; most
notably, VRDP improves the accuracy of predictive and counterfactual questions
by 4.5% and 11.5% compared to its best counterpart. VRDP is also highly
data-efficient: physical parameters can be optimized from very few videos, and
even a single video can be sufficient. Finally, with all physical parameters
inferred, VRDP can quickly learn new concepts from a few examples.
