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

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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

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