Modeling stochastic dynamical systems for interactive simulation

We present techniques for constructing approximate stochastic models of com plicated dynamical systems for applications in interactive computer graphic s. The models are designed to produce realistic interaction at low cost. We describe two kinds of stochastic models: continuous state (ARX) models a nd discrete state (Markov chains) models. System identification techniques are used for learning the input-output dynamics automatically, from either measurements of a real system or from an accurate simulation. The synthesis of behavior in this manner is several orders of magnitude faster than phys ical simulation. We demonstrate the techniques with two examples: (1) the d ynamics of candle flame in the wind, modeled using data from a real candle and (2) the motion of a falling leaf, modeled using data from a complex sim ulation. We have implemented an interactive Java program which demonstrates real-time interaction with a realistically behaving simulation of a cartoo n candle flame. The user makes the flame animation flicker by blowing into a microphone.