Differentiable Genetic Programming

TL;DR

This paper presents a novel differentiable genetic programming framework using high-order automatic differentiation, enabling more effective symbolic regression, differential equation solving, and dynamical system analysis.

Contribution

Introduces differentiable Cartesian Genetic Programming (dCGP) using high-order automatic differentiation for improved symbolic regression and dynamical system analysis.

Findings

dCGP accurately finds symbolic expressions and constants.

dCGP effectively solves differential equations.

dCGP identifies prime integrals of dynamical systems.

Abstract

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic regression, dCGP offers a new approach to the long unsolved problem of constant representation in GP expressions. On several problems of increasing complexity we find that dCGP is able to find the exact form of the symbolic expression as well as the constants values. We also demonstrate the use of dCGP to solve a large class of differential equations and to find prime integrals of dynamical systems, presenting, in both cases, results that confirm the efficacy of our approach.