17 September 2007

Reverse engineering nonlinear systems

(Note to self)

Bongard J., Lipson H. (2007), "Automated reverse engineering of nonlinear dynamical systems", Proceedings of the National Academy of Science, vol. 104, no. 24, pp. 9943-9948.


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.

(Another note to self)

Dear Future Gregg,

Young grasshopper, yo must resist the urge to buy songs like Rihanna's "Umbrella" and "Shut Up and Drive" from iTunes at 11pm. However, purchasing tunes like "Axel F" is just fine.

-Past Gregg

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