Learning Fast Neural Network Emulators
for Physics-based Models

Radek Grzeszczuk, Demetri Terzopoulos, and Geoffrey Hinton
Department of Computer Science, University of Toronto

Animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally very demanding. This paper demonstrates the viability of replacing the numerical simulation of model dynamics with a dramatically more efficient alternative. In particular, we propose a radically different approach to creating physically realistic animation that exploits fast emulators implemented as neural networks, which we call NeuroAnimators. NeuroAnimators are automatically trained off-line to emulate the actions of physics-based models, by observing the models in action. We demonstrate NeuroAnimators that have learned the motion not only of simple passive and active dynamic models, but also of state-of-the-art physics-based models reported in the literature, including mechanical models of a swimming dolphin and a running human. Depending on the model, our approach yields physically faithful animation one or two orders of magnitude faster than the conventional, numerical simulation technique.

We employ the backpropagation algorithm [1] to train feedforward networks to efficiently predict the state transitions of the numerically simulated dynamical models. To gain additional efficiency, we train the networks to predict ``super timesteps'', one or two orders of magnitude larger than the timestep used for the competing (implicit) numerical simulator, thus accruing outstanding efficiency without serious loss of accuracy. Figures 1 and 2 show frames from animations that illustrate the technique for different non-trivial dynamical systems.

Figure 1: This plate illustrates the emulation of 3 different dynamical systems: a three-link pendulum, an elastic cube and a biomechanical dolphin. In each display, the physical model is indicated by the Siggraph logo. In the third image the biomechanical dolphin [2] is in the background.

Figure 2: Emulated motion produced by training a NeuroAnimator on state transition data generated by the numerically simulated (by SD-Fast) Hodgins mechanical runner model [3].


  1. ``Learning internal representations by error backpropagation'', Rumelhart, D. E. and Hinton, G. E. and Williams, R. J., in ``Parallel Distributed Processing: Explorations in the Microstructure of Cognition'', MIT Press, 1986, ed. Rumelhart, D. E. and McCleland, J. L. and the PDP Research Group, vol. 1, 318-362.

  2. ``Automated learning of muscle-actuated locomotion through control abstraction,'' R. Grzeszczuk, D. Terzopoulos, Proc. ACM SIGGRAPH'95 Conference, Los Angeles, CA, August, 1995, in Computer Graphics Proceedings, Annual Conference Series, 1995, 63-70.

  3. ``Animating Human Athletics'', Jessica K. Hodgins and Wayne L. Wooten and David C. Brogan and James F. O'Brien, Proc. ACM SIGGRAPH'95 Conference, Los Angeles, CA, August, 1995, in Computer Graphics Proceedings, Annual Conference Series, 1995, 71-78.