  Differentiable physics is a powerful approach to learning and control
problems that involve physical objects and environments. While notable progress
has been made, the capabilities of differentiable physics solvers remain
limited. We develop a scalable framework for differentiable physics that can
support a large number of objects and their interactions. To accommodate
objects with arbitrary geometry and topology, we adopt meshes as our
representation and leverage the sparsity of contacts for scalable
differentiable collision handling. Collisions are resolved in localized regions
to minimize the number of optimization variables even when the number of
simulated objects is high. We further accelerate implicit differentiation of
optimization with nonlinear constraints. Experiments demonstrate that the
presented framework requires up to two orders of magnitude less memory and
computation in comparison to recent particle-based methods. We further validate
the approach on inverse problems and control scenarios, where it outperforms
derivative-free and model-free baselines by at least an order of magnitude.
