So this has become a problem in optimal control, and we have to boundary conditions (input/output data)? Specifically, find a control function (so the weights

So this has become a problem in optimal control, and we have to boundary conditions (input/output data)? Specifically, find a control function (so the weights of the activation function) which maps the system to your desired output? Then there are also much better ways to solve two point boundary problems rather than just shooting forward. [0] Is a good place to start, (although its old). [0] Numerical Methods for Two-Point Boundary-Value Problems. Herbert Keller.