Abstract: In a computational environment including at least one processor, an example method of reducing the number of symbolic parameters in a model of a physical system includes receiving an initial model such as a system of differential algebraic equations (DAEs), eliminating isolated symbolic parameters (if any) from the initial model, extracting parameter sub-expressions from the DAEs, establishing minimal disconnected clusters of parameter sub-expressions, and for each cluster, attempting to generate a reduced cluster having a reduced number of symbolic parameters using one or more algorithms. If more than one approach is successful, that which is most successful in reducing the number of symbolic parameters is selected. A revised model is created having fewer symbolic parameters than the initial model and based on simulation results obtained from the revised model, a prototype of a physical system is manufactured and/or changes are made to an existing physical system.

Abstract: An example method of simplifying a system expressed as differential algebraic equations includes transforming the differential algebraic equations into Hessenberg form, the Hessenberg form including algebraic equations and differential equations, using the algebraic equations to express a constraint manifold, and using a combination of differentiation and projections onto the normal and tangential spaces of the constraint manifold to simplify the differential equations.

Abstract: An example method of simplifying a system expressed as differential algebraic equations includes transforming the differential algebraic equations into Hessenberg form, the Hessenberg form including algebraic equations and differential equations, using the algebraic equations to express a constraint manifold, and using a combination of differentiation and projections onto the normal and tangential spaces of the constraint manifold to simplify the differential equations.

Abstract: In a computational environment including at least one processor, an example method of reducing the number of parameters in a model of a physical system includes receiving an initial model such as a system of differential algebraic equations (DAEs), eliminating isolated parameters (if any) from the initial model, extracting parameter sub-expressions from the DAEs, establishing minimal disconnected clusters of parameter subexpressions, and for each cluster, attempting to generate a reduced cluster having a reduced number of parameters using one or more algorithms. If more than one approach is successful, that which is most successful in reducing the number of parameters is selected. A revised model is created having fewer parameters than the initial model.