Modeling Stochastic Dynamical Systems for Interactive Simulation

We describe two kinds of stochastic models: continuous state (ARX) models and discrete state (Markov chains) models. System identi cation 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 physical simulation.We demonstrate the techniques with two examples: (1) the dynamics of candle ame in the wind, modeled using data from a real candle and (2) the motion of a falling leaf, modeled using data from a complex simulation. We have implemented an interactive Java program which demonstrates real-time interaction with a realistically behaving simulation of a cartoon candle ame. The user makes the ame animation icker by blowing into a microphone.