Computing edge weights of a graph from time-series data of nodes

I've the following system of equations for studying information flow in the below graph,

dI/dt = - M^TDM* I

I is the vector with variables [ A B C D E F]

M is the incidence matrix

and I want to determine the value of diagonal elements in the matrix D. The entries in the

diagonal elements are the edge weights.

The data that I have is the time-series values of the property " I " at every node.

I'd like to know if there is a way to solve this as an optimization problem using fmicon in MATLAB.

Any suggestions will be really helpful