While normally I would also try to do my best to find an existing protocol that covers this, the kind of data used in numerical works (potentially nested, multidimensional arrays, complex elements) is not well supported by simple formats so rolling your own (to a certain extent) may be the most viable alternative.
For Vector{Vector} etc, I would invest in either flattening to a higher dimensional array (eg Matrix) for regular sizes, or a ragged structure for irregular sizes (a flat Vector, and a bunch of indexes).