Differentiable Implicit Soft-Body Physics

We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state transitions, we focus on implicit state transitions defined via function minimization. Implicit state transitions appear in implicit numerical integration methods, which offer the benefits of large time steps and excellent numerical stability, but require a special treatment to achieve differentiability due to the absence of an explicit differentiable forward pass. In contrast to other implicit differentiation approaches that require explicit formulas for the force function and the force Jacobian matrix, we present an energy-based approach that allows us to compute these derivatives automatically and in a matrix-free fashion via reverse-mode automatic differentiation. This allows for more flexibility and productivity when defining physical models and is particularly important in the context of neural network training, which often relies on reverse-mode automatic differentiation (backpropagation). We demonstrate the effectiveness of our differentiable simulator in policy optimization for locomotion tasks and show that it achieves better sample efficiency than model-free reinforcement learning.