TY - GEN
T1 - Faster Groebner bases for Lie derivatives of ODE systems via monomial orderings
AU - Bessonov, Mariya
AU - Ilmer, Ilia
AU - Konstantinova, Tatiana
AU - Ovchinnikov, Alexey
AU - Pogudin, Gleb
AU - Soto, Pedro
N1 - Publisher Copyright:
© 2024 ACM.
PY - 2024/7/16
Y1 - 2024/7/16
N2 - Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze these models is to compute and then symbolically process the polynomial system obtained by sufficiently many Lie derivatives of the output functions with respect to the vector field given by the ODE system. In this paper, we present a method for speeding up Gröbner basis computation for such a class of polynomial systems by using specific monomial ordering, including weights for the variables, coming from the structure of the ODE model. We provide empirical results that show improvement across different symbolic computing frameworks and apply the method to speed up structural identifiability analysis of ODE models.
AB - Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze these models is to compute and then symbolically process the polynomial system obtained by sufficiently many Lie derivatives of the output functions with respect to the vector field given by the ODE system. In this paper, we present a method for speeding up Gröbner basis computation for such a class of polynomial systems by using specific monomial ordering, including weights for the variables, coming from the structure of the ODE model. We provide empirical results that show improvement across different symbolic computing frameworks and apply the method to speed up structural identifiability analysis of ODE models.
KW - F4 algorithm
KW - ODE Systems
KW - differential algebra
KW - mathematical biology
KW - parameter identifiability
KW - weighted monomial ordering
U2 - 10.1145/3666000.3669695
DO - 10.1145/3666000.3669695
M3 - Conference contribution
AN - SCOPUS:85199517629
T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
SP - 234
EP - 243
BT - ISSAC 2024 - Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation
A2 - Chen, Shaoshi
PB - Association for Computing Machinery
T2 - 49th International Symposium on Symbolic and Algebraic Computation, ISSAC 2024
Y2 - 16 July 2024 through 19 July 2024
ER -