TY - GEN
T1 - Genetic programming and automatic differentiation algorithms applied to the solution of ordinary and partial differential equations
AU - Lobao, Waldir J.A.
AU - Dias, Douglas Mota
AU - Pacheco, Marco Aurelio C.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/11/14
Y1 - 2016/11/14
N2 - This paper investigates the potential of evolutionary algorithms, developed by the combination of genetic programming (GP) and automatic differentiation methods (AD), in determining analytic solutions to ordinary and partial differential equations (ODE and PDE). In turn, AD is a set of techniques based on the mechanical application of the chain rule to numerically evaluate the derivative of a function specified by a computer program. The AD method has a fundamental role in this work since it calculates the exact values of the derivatives of a function for a given set of input values while numerical differentiation methods introduce unacceptable round-off errors in the discretization process. With this purpose, and using the Matlab programming environment, we developed several algorithms (namely GPAD) and addressed problems of different kinds of differential equations. The results are promising, with exact solutions obtained for most of the addressed problems, which include equations where not even commercial systems could find a symbolic solution. These results empirically indicate that GPAD can be an efficient and robust methodology to find analytic solutions for ODE and PDE.
AB - This paper investigates the potential of evolutionary algorithms, developed by the combination of genetic programming (GP) and automatic differentiation methods (AD), in determining analytic solutions to ordinary and partial differential equations (ODE and PDE). In turn, AD is a set of techniques based on the mechanical application of the chain rule to numerically evaluate the derivative of a function specified by a computer program. The AD method has a fundamental role in this work since it calculates the exact values of the derivatives of a function for a given set of input values while numerical differentiation methods introduce unacceptable round-off errors in the discretization process. With this purpose, and using the Matlab programming environment, we developed several algorithms (namely GPAD) and addressed problems of different kinds of differential equations. The results are promising, with exact solutions obtained for most of the addressed problems, which include equations where not even commercial systems could find a symbolic solution. These results empirically indicate that GPAD can be an efficient and robust methodology to find analytic solutions for ODE and PDE.
UR - https://www.scopus.com/pages/publications/85008256498
U2 - 10.1109/CEC.2016.7748362
DO - 10.1109/CEC.2016.7748362
M3 - Conference contribution
AN - SCOPUS:85008256498
T3 - 2016 IEEE Congress on Evolutionary Computation, CEC 2016
SP - 5286
EP - 5292
BT - 2016 IEEE Congress on Evolutionary Computation, CEC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE Congress on Evolutionary Computation, CEC 2016 - Part of 2016 IEEE World Congress on Computational Intelligence, WCCI 2016
Y2 - 24 July 2016 through 29 July 2016
ER -