  We present a method for fast and accurate physics-based predictions during
non-prehensile manipulation planning and control. Given an initial state and a
sequence of controls, the problem of predicting the resulting sequence of
states is a key component of a variety of model-based planning and control
algorithms. We propose combining a coarse (i.e. computationally cheap but not
very accurate) predictive physics model, with a fine (i.e. computationally
expensive but accurate) predictive physics model, to generate a hybrid model
that is at the required speed and accuracy for a given manipulation task. Our
approach is based on the Parareal algorithm, a parallel-in-time integration
method used for computing numerical solutions for general systems of ordinary
differential equations. We adapt Parareal to combine a coarse pushing model
with an off-the-shelf physics engine to deliver physics-based predictions that
are as accurate as the physics engine but run in substantially less wall-clock
time, thanks to parallelization across time. We use these physics-based
predictions in a model-predictive-control framework based on trajectory
optimization, to plan pushing actions that avoid an obstacle and reach a goal
location. We show that with hybrid physics models, we can achieve the same
success rates as the planner that uses the off-the-shelf physics engine
directly, but significantly faster. We present experiments in simulation and on
a real robotic setup. Videos are available here: https://youtu.be/5e9oTeu4JOU

Robotics