Faster Gr\"obner Bases via Domain-Specific Ordering in Parameter Identifiability of ODE Models

We consider a specific class of polynomial systems that arise in parameter identifiability problems of models of ordinary differential equations (ODE) and discover a method for speeding up the Gr\"obner basis computation by using specific variable ordering and weights coming from the structure of the ODE model. We provide empirical results that show improvement across different symbolic computing frameworks.