Automated reverse engineering of nonlinear dynamical systems Export

@article{citeulike:1381981, abstract = {10.1073/pnas.0609476104 Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. 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 ” reverse engineering” 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.}, author = {Bongard, Josh and Lipson, Hod}, citeulike-article-id = {1381981}, citeulike-linkout-0 = {http://dx.doi.org/10.1073/pnas.0609476104}, citeulike-linkout-1 = {http://www.pnas.org/content/104/24/9943.full.abstract}, citeulike-linkout-2 = {http://www.pnas.org/content/104/24/9943.full.full.pdf}, citeulike-linkout-3 = {http://www.pnas.org/cgi/content/abstract/104/24/9943}, citeulike-linkout-4 = {http://view.ncbi.nlm.nih.gov/pubmed/17553966}, citeulike-linkout-5 = {http://www.hubmed.org/display.cgi?uids=17553966}, day = {12}, doi = {10.1073/pnas.0609476104}, journal = {Proceedings of the National Academy of Sciences}, keywords = {dynamics, model}, month = {June}, number = {24}, pages = {9943--9948}, posted-at = {2009-04-16 19:25:47}, priority = {5}, title = {Automated reverse engineering of nonlinear dynamical systems}, url = {http://dx.doi.org/10.1073/pnas.0609476104}, volume = {104}, year = {2007} }

TY - JOUR ID - citeulike:1381981 L3 - citeulike-article-id:1381981 N2 - 10.1073/pnas.0609476104 Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. 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 “reverse engineering” 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. IS - 24 JF - Proceedings of the National Academy of Sciences EP - 9948 TI - Automated reverse engineering of nonlinear dynamical systems VL - 104 SP - 9943 KW - dynamics KW - model AU - Bongard, Josh AU - Lipson, Hod PY - 2007/06/12/ UR - http://dx.doi.org/10.1073/pnas.0609476104 ER -