Embodiments provide methods and systems for constructing surrogate models for use in interactive experiences. One such embodiment begins by defining a model that includes a parametric state vector and a design variable vector and represents a real world system. Next, a first and second experiment are performed to determine a response over time of the parametric state vector and to produce a dataset of the parametric state vector and the design variable vector as a function of time. The dataset is then modified with one or more derivatives of the parametric state vector and a set of surrogate differential equations is constructed that approximates a higher derivative of the parametric state vector relative to that in the dataset and the set of surrogate differential equations is stored as a surrogate model. The surrogate model is in turn provided from memory in a manner accelerating simulated behavior in response to user-interaction with the model.