Clever DAE: Compiler Optimizations for Digital Twins at Scale

Modeling and simulation are fundamental activities in engineering to facilitate prototyping, verification and maintenance. Declarative modeling languages allow to simulate physical phenomena by expressing them in terms of Differential and Algebraic Equations (DAE) systems. In this paper, we focus on the problem of generating code for performing the numerical integration of the model equations, and in particular on the overhead introduced by external numerical solver libraries. We propose a novel methodology for minimizing the amount of equations which require to be solved through an external solver library, together with the number of computations that are required to computed the Jacobian matrix of the system. Through a prototype LLVM-based compiler, we demonstrate how this approach achieves a linear speed-up in simulation time with respect to the baseline.