Speaker
Description
Industrial manufacturing processes are often described by systems of differential equations with respective material laws. Since these material laws depend on material-specific parameters, which are frequently unknown or can only be obtained through a range of expensive experiments, there is a need for numerical parameter estimation strategies. In this context, we consider a fiber spinning process modeled by a boundary value problem (BVP) of ordinary differential equations where a certain material law needs to be estimated on the basis of few experimental data. First, we consider the problem where the structural form of the material law is known. We have developed a numerical method involving collocation and continuation methods to solve BVPs that arise in a generalized Newtonian setting. Furthermore, we are able to calculate gradients of the BVP solutions with respect to the material parameters and apply nonlinear optimization techniques to optimize the material parameters of interest with respect to given measurement data. In this talk our aim is to extend the approach to the case where the structural form of the material law is not known. We discuss arising difficulties and propose a method for estimating the values of the material law along the fiber to be able to frame the problem in the context of symbolic regression.
