A differential approach to solve the inverse eigenvalue problem derived from a neural network

We consider the problem of designing a general additive neural network which possesses prescribed equilibria. The relation between this design problem and a problem of generating a matrix with specified eiegenvalues, which maps a given set of vectors of another given set, is investigated. The obtained inverse eigenvalue problem is then solved using a gradient flow approach. Working with discretisation of systems of differential equations allows to preserve the original dimension of the problem and could give the possibility of constructing adaptive schemes faster than algebraic one.