DifferentialEquations.jl can take as many simultaneous equations as you have memory for. You can even use an MPIArray when you run out. When we solve PDEs, some

DifferentialEquations.jl can take as many simultaneous equations as you have memory for. You can even use an MPIArray when you run out. When we solve PDEs, sometimes I'm testing with a state space of tens of millions of ODEs of course, which comes from a Method of Lines discretization. Right now we are doing a lot of tests in the thousands of ODEs range since we have a reader for chemical reaction networks which we are using to optimize on test models. This is all with directly writing the Julia functions. If you question is, how far can ModelingToolkit be pushed? That's unknown. We made sure it's quite an efficient representation, but we haven't stress tested it to see the memory consumption at a million operations yet. Since it's able to generate thousands of operations in symbolic Jacobian inversions, it easy goes to thousands and tens of thousands of equations. How much larger? Who knows. What we can say is that its efficiency is more similar to SymEngine's symbolic types, so if SymEngine handles the millions of equations range (on a computer with enough RAM, symbolic representations may use up quite a bit here!) than we should be able to.