Ponente
Descripción
Symbolic Regression (SR) for Ordinary Differential Equations (ODE) can be used to identify the ODE that best fits a dynamical system described by observed data. One way to implement the SR is using meta-heuristics to explore the space of possible expressions for the right hand side of the ODE. In this work, we present a method to narrow the search space when the right-hand side of the ODE is assumed to be linear with respect to the parameters. The search space is reduced by identifying certain properties of the right hand side. Those properties are: which of the observed variables appear in the right hand function, what is the degree of each variable in the function (that is assumed to be a polynomial), and whether a variable appears in all terms of the right hand side. To check these properties we designed a neural network to interpolate the right hand side of the system using the observed data. The desired properties are checked by evaluating the neural network at different points. If it is determined that the right side of the system satisfies some of these properties, then the search space is reduced to those functions that satisfy them. The noise-free experiments carried out in this work with different systems of differential equations show that it is possible to reduce the search space, although in some cases (as in the SIR model) we need to generate data from different initial conditions.
