Many systems both in nature and created by humans give rise to time series data with complex, nonlinear dynamics. Moreover, such time series can cover different dynamical regimes which identification is of pivotal importance in system modeling. Ordinary differential equations with switching provide a tool for modeling physical phenomena whose time series data exhibit different dynamical modes. Usually, these modes are determined by changing unmeasured parameters of the system that should be learned from the available data. The paper proposes a novel learning structure in polynomial neural network (PNN) basis suitable for parametric identification of dynamical systems and doesn’t require usage of numerical integration methods. The PNN weight matrices incorporate the information about the parameters of ODEs and vice versa the unknown parameters of ODEs can be recovered from the PNN weights. Transferring the knowledge about the particular states dependencies in ODEs to PNN can be carried out by finding the initial weight matrices of PNN. The paper proposes a method for PNN initialization based an iterative procedure for step by step non stationary ODE flow computing in the polynomial form. However, even when the ODEs are unknown, PNN can be learned from scratch and provide parameter identification for ODEs. We evaluate the proposed approach on synthetic dataset generated with the system of ODEs for an electrostatical deflector. As a result, PNN successfully uncovers different dynamical regimes and predict the switching dynamics for different initial conditions outside the training data range.