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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\u2013environment 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.<\/jats:p>","DOI":"10.1177\/0278364915576336","type":"journal-article","created":{"date-parts":[[2015,5,28]],"date-time":"2015-05-28T20:17:24Z","timestamp":1432844244000},"page":"1278-1295","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":30,"title":["Probabilistically valid stochastic extensions of deterministic models for systems with uncertainty"],"prefix":"10.1177","volume":"34","author":[{"given":"Konstantinos","family":"Karydis","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, DE, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis","family":"Poulakakis","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, DE, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianxin","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, DE, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herbert G.","family":"Tanner","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Delaware, Newark, DE, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,5,28]]},"reference":[{"key":"bibr1-0278364915576336","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2005.I.038"},{"key":"bibr2-0278364915576336","unstructured":"Abu-Mostafa YS, Magdon-Ismail M, Lin HT (2012) Learning From Data. 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