>BTW, I have heard it said there is also no reasonable human explanation for quantum mechanics,

This is true if you were quoting Feynman, may he rest in peace. The proposed algebras that model quantum behaviour are human cognizable but the results obtained from them are not e.g. quantum tunneling or time reversal.

So the written code that does certain algorithm is human cognizable but the results it produces are not! This is almost true for any application of Machine Learning and Machine Vision as well, that humans could not explain the output of these code/algorithms. Yet the results are useful and model some dynamical systems well.

If we remove the code and the algorithm and try to explain how to navigate a UAV in a storm or how to balance a 1-legged robot or how to fly an airplane with a broken damaged wing, we cannot.

Almost the same is true for solutions to a system of differential equations.

So my comment to you was: DO USE SLOSHING like arguments and computations, but we do not have to be stuck with known formulas or patterns of behaviour to model a dynamical system.