Abstract: We present a new method for efficiently approximating the global penetration depth between two rigid objects using machine learning techniques. Our approach consists of two phases: offline learning and performing run-time queries. In the learning phase, we precompute an approximation of the contact space of a pair of intersecting objects from a set of samples in the configuration space. We use active and incremental learning algorithms to accelerate the precomputation and improve the accuracy. During the run-time phase, our algorithm performs a nearest-neighbor query based on translational or rotational distance metrics. The run-time query has a small overhead and computes an approximation to global penetration depth in a few milliseconds. We use our algorithm for collision response computations in Box2D or Bullet game physics engines and complex 3D models and observe more than an order of magnitude improvement over prior PD computation techniques.