Fast, stable physics simulation for robots and soft materials

Simulating soft bodies with different material properties is essential for robot learning and trajectory optimization, but existing differentiable simulators fail on heterogeneous materials with stiffness ratios exceeding 10–100× or large deformations. DiffPhD combines stiffness-aware weighting, stabilized gradient computation via eigenvalue filtering and Anderson acceleration, and a GPU pipeline that reuses sparse matrix factors across forward, backward, and contact steps. On benchmarks involving composite structures, soft characters with rigid props, and gripper manipulation, the method achieves order-of-magnitude speedups while remaining convergent at 100× stiffness contrast, where prior solvers degrade. Code and models are released.