Genetic Programming and Evolvable Machines

, Volume 14, Issue 2, pp 155-190

First online:

Inference of hidden variables in systems of differential equations with genetic programming

  • Theodore W. CornforthAffiliated withBiological Statistics and Computational Biology, Cornell University Email author 
  • , Hod LipsonAffiliated withMechanical and Aerospace Engineering, Cornell University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


The data-driven modeling of dynamical systems is an important scientific activity, and many studies have applied genetic programming (GP) to the task of automatically constructing such models in the form of systems of ordinary differential equations (ODEs). These previous studies assumed that data measurements were available for all variables in the system, whereas in real-world settings, it is typically the case that one or more variables are unmeasured or “hidden.” Here, we investigate the prospect of automatically constructing ODE models of dynamical systems from time series data with GP in the presence of hidden variables. Several examples with both synthetic and physical systems demonstrate the unique challenges of this problem and the circumstances under which it is possible to reverse-engineer both the form and parameters of ODE models with hidden variables.


Genetic programming Ordinary differential equations Hidden variables Modeling Symbolic identification