Building probabilistic models of physical processes from their deterministic models and some experimental data, with guarantees on the degree of coincidence between the generated model and the real system

Konstantinos Karydis, Ioannis Poulakakis, Jianxin Sun, and Herbert G. Tanner, Probabilistically valid stochastic extensions of deterministic models for systems with uncertainty, The International Journal of Robotics Research September 2015 34: 1278-1295, first published on May 28, 2015. DOI: 10.1177/0278364915576336.

Models capable of capturing and reproducing the variability observed in experimental trials can be valuable for planning and control in the presence of uncertainty. This paper reports on a new data-driven methodology that extends deterministic models to a stochastic regime and offers probabilistic guarantees of model fidelity. From an acceptable deterministic model, a stochastic one is generated, capable of capturing and reproducing uncertain system–environment interactions at given levels of fidelity. The reported approach combines methodological elements from probabilistic model validation and randomized algorithms, to simultaneously quantify the fidelity of a model and tune the distribution of random parameters in the corresponding stochastic extension, in order to reproduce the variability observed experimentally in the physical process of interest. The approach can be applied to an array of physical processes, the models of which may come in different forms, including differential equations; we demonstrate this point by considering examples from the areas of miniature legged robots and aerial vehicles.

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