A neural network system for identifying forecasting, and controlling a non-linear flow on a physical system network, in which each branch between nodes in the physical system network is divided by a plurality of division points; a flow at each of the division points and a terminal point of each branch is calculated according to neural network model parameters specifying connections among the division points and the terminal point in a neural network model; an actual flow is measured at the terminal point of said each branch; an error of the calculated flow at the terminal point with respect to the measured actual flow at the terminal point is calculated; the neural network model parameters are adjusted to minimize the calculated error; and system dynamics parameters specifying dynamics of the physical system are determined according to the adjusted neural network model parameters. In addition, a target function to be optimized is calculated in terms of flows at terminal points of branches as a function of a control parameter specifying connecting and disconnecting of connections among branches at each node; and connections among branches at each node are connected/disconnected to optimize the calculated target function.