I have a network of agents, these are modeled roughly according to the paradigm of "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science". The main feature is that the equations for the states of each agent is
agent_i^(t+1) = a*f1(agent_i^t) + b*f2(agents_(j excluding i)^t)
My model is not exactly like this, as I am looking at these functions as discretized versions of the SDE components for the trajectory. Here, f1 and f2 are based upon the states of the agent and surrounding agents respectively as linear projections upon some fixed constants.
The question is given some data for the state value of each agent/node at the time points (between 0 and 1), what are the techniques to best fit the parameters $(a,b)$? These can be put into a OLS (ordinary least squares) search, but are there other methods to consider?