Differentiable Physics

Differentiable physics studies how to compute gradients through simulations of systems such as rigid-body contact, deformable materials, fluids, and chemical processes. Common approaches differentiate numerical solvers with automatic differentiation, adjoints, or implicit differentiation, and combine FEM, MPM, or PDE solvers with learned models; smoothing is often used for contacts and discrete events. These gradients support inverse problems, where observations are used to infer physical parameters, as well as trajectory optimization and control in settings such as robot manipulation and fluid engineering. GPU acceleration is making larger simulations practical, but gradients can still be unreliable around contact and other discontinuities, and speed must be balanced against physical fidelity and numerical stability.