Development of accurate models for analysis and prediction lies at the core of any engineering application. Ordinary and partial differential equations (ODEs \& PDEs) represent a natural approach to this task. Typically, however, we lack complete understanding of a given process and thus the derived differential equations yield limited accuracy. In this work, we propose a new workflow centered around universal differential equations (UDEs), allowing us to build upon existing knowledge (in the form of ODEs / PDEs) and extending it via neural networks (NNs) into UDEs. By exploiting the small size of the employed NN, we reduce its contribution to a sum of simple nonlinear polynomial terms, using the method of sparse identification of nonlinear dynamical systems (SINDy). This polynomial representation of the NN is then reinserted into the original ODE, yielding an augmented version of itself (exODE), which is again purely analytical. The presented workflow therefore enables building upon existing knowledge in a data driven manner and can be applied to any problem for which (limited) pre-knowledge is available in the form of an ODE or PDE.