Discovering Symmetries of ODEs by Symbolic Regression
This work addresses a specific bottleneck in automated ODE solving for researchers in dynamical systems and computer algebra, though it is incremental as it builds on existing symbolic regression methods.
The authors tackled the problem of finding Lie point symmetries for ordinary differential equations (ODEs), which is challenging for computer algebra systems, by adapting search-based symbolic regression to discover symmetry generators, enabling the identification of symmetries that existing systems cannot find.
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra systems (CASs) provide support for solving ODEs by first simplifying them, in particular through the use of Lie point symmetries. Finding these symmetries is, however, itself a difficult problem for CASs. Recent works in symbolic regression have shown promising results for recovering symbolic expressions from data. Here, we adapt search-based symbolic regression to the task of finding generators of Lie point symmetries. With this approach, we can find symmetries of ODEs that existing CASs cannot find.