In this work, we study the augmentation of a novel differentiable rigid-body physics engine via neural networks that is able to learn nonlinear relationships between dynamic quantities and can thus learn  ...  We observe a ten-fold speed-up when replacing the QP solver inside a model-predictive gait controller for quadruped robots with a neural network, allowing us to significantly improve control delays as  ...  Right: augmentation of differentiable simulators with our proposed neural scalar type where variable e becomes a combination of an analytical model φ (·, ·) with inputs a and b, and a neural network whose  ...