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This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated \u201creverse engineering\u201d approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.<\/jats:p>","DOI":"10.1073\/pnas.0609476104","type":"journal-article","created":{"date-parts":[[2007,6,6]],"date-time":"2007-06-06T20:54:51Z","timestamp":1181163291000},"page":"9943-9948","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":651,"title":["Automated reverse engineering of nonlinear dynamical systems"],"prefix":"10.1073","volume":"104","author":[{"given":"Josh","family":"Bongard","sequence":"first","affiliation":[{"name":"*Mechanical and Aerospace Engineering and"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hod","family":"Lipson","sequence":"additional","affiliation":[{"name":"*Mechanical and Aerospace Engineering and"},{"name":"Computing and Information Science, Cornell University, Ithaca, NY 14853"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2007,6,12]]},"reference":[{"key":"e_1_3_3_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471722146"},{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781118625590"},{"key":"e_1_3_3_3_2","volume-title":"System Identification: Theory for the User","author":"Ljung L","year":"1999","unstructured":"L Ljung System Identification: Theory for the User (Prentice\u2013Hall, Englewood Cliffs, NJ, 1999)."},{"key":"e_1_3_3_4_2","volume-title":"Phys Rev E","author":"McKinney BA","year":"2006","unstructured":"BA McKinney, JE Crowe, HU Voss, PS Crooke, N Barney, JH Moore Phys Rev E 73, 021912(1\u20137). 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